2002, Lecture notes in mathematics, ISBN 3540437983, Volume 1790., vi, 116

Book

IEEE transactions on automatic control, ISSN 1558-2523, 2015, Volume 60, Issue 10, pp. 2768 - 2772

The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use...

Free-matrix-based integral inequality | time-varying delay | Symmetric matrices | Upper bound | Stability criteria | Educational institutions | Lyapunov-Krasovskii functional | Vectors | time delay system | Delays | Linear matrix inequalities | stability | CRITERIA | H-INFINITY CONTROL | ROBUST STABILITY | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Delay lines | Analysis | Stability | Integrals | Inequalities | Automatic control | Transformations | Stability analysis | Criteria | Delay

Free-matrix-based integral inequality | time-varying delay | Symmetric matrices | Upper bound | Stability criteria | Educational institutions | Lyapunov-Krasovskii functional | Vectors | time delay system | Delays | Linear matrix inequalities | stability | CRITERIA | H-INFINITY CONTROL | ROBUST STABILITY | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Delay lines | Analysis | Stability | Integrals | Inequalities | Automatic control | Transformations | Stability analysis | Criteria | Delay

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2011, Volume 57, Issue 4, pp. 2342 - 2359

This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries...

oracle inequalities and semidefinite programming | matrix completion | Noise | Measurement uncertainty | Convex optimization | Minimization | norm of random matrices | Linear matrix inequalities | Noise measurement | Sparse matrices | Compressed sensing | Dantzig selector | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Matrices | Research | Information theory

oracle inequalities and semidefinite programming | matrix completion | Noise | Measurement uncertainty | Convex optimization | Minimization | norm of random matrices | Linear matrix inequalities | Noise measurement | Sparse matrices | Compressed sensing | Dantzig selector | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Matrices | Research | Information theory

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 4, pp. 2512 - 2539

...) of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality...

Computer algebra algorithms | Semidefinite programming | Linear matrix inequalities | Polynomial optimization | Symbolic computation | MATHEMATICS, APPLIED | symbolic computation | computer algebra algorithms | SUMS | semidefinite programming | POLYNOMIALS | linear matrix inequalities | COMPLEXITY | SETS | polynomial optimization | SYSTEMS | OPTIMIZATION | COMPUTATION | SQUARES | GEOMETRY | Mathematics | Optimization and Control | Symbolic Computation | Computer Science

Computer algebra algorithms | Semidefinite programming | Linear matrix inequalities | Polynomial optimization | Symbolic computation | MATHEMATICS, APPLIED | symbolic computation | computer algebra algorithms | SUMS | semidefinite programming | POLYNOMIALS | linear matrix inequalities | COMPLEXITY | SETS | polynomial optimization | SYSTEMS | OPTIMIZATION | COMPUTATION | SQUARES | GEOMETRY | Mathematics | Optimization and Control | Symbolic Computation | Computer Science

Journal Article

IEEE transactions on automatic control, ISSN 1558-2523, 2009, Volume 54, Issue 5, pp. 952 - 964

Most linear control problems lead directly to matrix inequalities (MIs). Many of these are badly behaved but a classical core of problems are expressible as linear matrix inequalities (LMIs...

Linear systems | linear control systems | Optimization methods | Linear programming | Control systems | linear matrix inequality (LMI) | Mathematics | Linear matrix inequalities | Geometry | Systems engineering and theory | convex optimization | Control theory | Books | Algebraic approaches | Linear matrix inequality (LMI) | Convex optimization | Linear control systems | POLYNOMIALS | GLOBAL OPTIMIZATION | AUTOMATION & CONTROL SYSTEMS | STRICT POSITIVSTELLENSATZ | ENGINEERING, ELECTRICAL & ELECTRONIC | Inequalities (Mathematics) | Evaluation | Research | Design and construction | Mathematical optimization | Studies | Mathematical analysis | Inequalities | Automatic control | Matrices | Convexity | Linear control

Linear systems | linear control systems | Optimization methods | Linear programming | Control systems | linear matrix inequality (LMI) | Mathematics | Linear matrix inequalities | Geometry | Systems engineering and theory | convex optimization | Control theory | Books | Algebraic approaches | Linear matrix inequality (LMI) | Convex optimization | Linear control systems | POLYNOMIALS | GLOBAL OPTIMIZATION | AUTOMATION & CONTROL SYSTEMS | STRICT POSITIVSTELLENSATZ | ENGINEERING, ELECTRICAL & ELECTRONIC | Inequalities (Mathematics) | Evaluation | Research | Design and construction | Mathematical optimization | Studies | Mathematical analysis | Inequalities | Automatic control | Matrices | Convexity | Linear control

Journal Article

Proceedings of the IEEE, ISSN 1558-2256, 2010, Volume 98, Issue 6, pp. 925 - 936

..., namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information...

Computer vision | low-rank matrices | Filtering | matrix completion | Linear matrix inequalities | Remote sensing | Noise level | semidefinite programming | oracle inequalities | Collaboration | nuclear-norm minimization | Machine learning | Motion pictures | Frequency | duality in optimization | Compressed sensing | Semidefinite programming | Duality in optimization | Nuclear-norm minimization | Oracle inequalities | Low-rank matrices | Matrix completion | INFORMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Studies | Noise | Minimization | Matrices | Detection | Compressed | Optimization | Quantitative analysis

Computer vision | low-rank matrices | Filtering | matrix completion | Linear matrix inequalities | Remote sensing | Noise level | semidefinite programming | oracle inequalities | Collaboration | nuclear-norm minimization | Machine learning | Motion pictures | Frequency | duality in optimization | Compressed sensing | Semidefinite programming | Duality in optimization | Nuclear-norm minimization | Oracle inequalities | Low-rank matrices | Matrix completion | INFORMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Studies | Noise | Minimization | Matrices | Detection | Compressed | Optimization | Quantitative analysis

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 10/2019, Volume 126, Issue 9, pp. 809 - 815

We describe a rather striking extension of a wide class of inequalities. Some famous classical inequalities, such as those of Hardy and Hilbert, equate to the evaluation of the norm of a matrix operator...

Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC

Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC

Journal Article

2006, Foundations and trends in communications and information theory, ISBN 160198040X, Volume 3, issue 6 (2006), Issue 6, ix, 153

...Abstract This short tutorial presents two mathematical techniques namely Majorization Theory and Matrix-Monotone Functions, reviews their basic definitions...

Book

IEEE Transactions on Automatic Control, ISSN 0018-9286, 02/2006, Volume 51, Issue 2, pp. 192 - 202

Using a moment interpretation of recent results on sum-of-squares decompositions of nonnegative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI...

Linear systems | State feedback | Optimization methods | polynomial matrix | Linear matrix inequalities | nonconvex optimization | Matrix decomposition | Design optimization | Linear feedback control systems | Convex optimization | Control system synthesis | Polynomials | static output feedback design | Output feedback | Nonconvex optimization | Polynomial matrix | Static output feedback design | SEDUMI | GLOBAL OPTIMIZATION | convex optimization | MATLAB | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Feedback control systems | Analysis | Bismaleimides | Lower bounds | Hierarchies | Inequalities | Automatic control | Polynomial matrices | Optimization

Linear systems | State feedback | Optimization methods | polynomial matrix | Linear matrix inequalities | nonconvex optimization | Matrix decomposition | Design optimization | Linear feedback control systems | Convex optimization | Control system synthesis | Polynomials | static output feedback design | Output feedback | Nonconvex optimization | Polynomial matrix | Static output feedback design | SEDUMI | GLOBAL OPTIMIZATION | convex optimization | MATLAB | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Feedback control systems | Analysis | Bismaleimides | Lower bounds | Hierarchies | Inequalities | Automatic control | Polynomial matrices | Optimization

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 09/2006, Volume 51, Issue 9, pp. 1506 - 1509

We present a family of eigenvalue inequalities for the product of a Hermitian matrix and a positive-semidefinite matrix...

inequality | Symmetric matrices | Upper bound | trace | Riccati equations | Eigenvalue | Eigenvalues and eigenfunctions | Linear matrix inequalities | Control theory | singular value | Trace | Singular value | Inequality | ALGEBRAIC RICCATI | SEMIDEFINITE HERMITIAN MATRICES | BOUNDS | LYAPUNOV EQUATIONS | eigenvalue | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Eigenvalues | Inequalities (Mathematics) | Analysis | Automatic control | Theorems | Inequalities

inequality | Symmetric matrices | Upper bound | trace | Riccati equations | Eigenvalue | Eigenvalues and eigenfunctions | Linear matrix inequalities | Control theory | singular value | Trace | Singular value | Inequality | ALGEBRAIC RICCATI | SEMIDEFINITE HERMITIAN MATRICES | BOUNDS | LYAPUNOV EQUATIONS | eigenvalue | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Eigenvalues | Inequalities (Mathematics) | Analysis | Automatic control | Theorems | Inequalities

Journal Article

11.
Full Text
Stability of Linear Systems With Time-Varying Delays Using Besselâ€“Legendre Inequalities

IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2018, Volume 63, Issue 1, pp. 225 - 232

.... Hierarchical stability conditions based on linear matrix inequalities are obtained from an extensive use of the Bessel inequality applied to Legendre polynomials of arbitrary orders...

Symmetric matrices | Stability criteria | stability analysis | Delays | Linear matrix inequalities | time-varying delay systems | integral inequality | Numerical stability | Time-varying systems | Allowable delay sets | Integral inequality | Stability analysis | Time-varying delay systems | CRITERIA | linear matrix inequalities | ROBUST STABILITY | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | DEPENDENT STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Engineering Sciences | Automatic

Symmetric matrices | Stability criteria | stability analysis | Delays | Linear matrix inequalities | time-varying delay systems | integral inequality | Numerical stability | Time-varying systems | Allowable delay sets | Integral inequality | Stability analysis | Time-varying delay systems | CRITERIA | linear matrix inequalities | ROBUST STABILITY | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | DEPENDENT STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Engineering Sciences | Automatic

Journal Article

Automatica, ISSN 0005-1098, 2010, Volume 46, Issue 8, pp. 1327 - 1333

.... The stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals...

Sampled-data control | Conservatism | Semidefinite programming | Robust linear matrix inequality | Asymptotic exactness | Adaptive division | RELAXATIONS | DELAY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Control systems | Analysis | Intervals | Stability | Stabilization | Stability analysis | Tightness | Linear matrix inequalities | Sampling

Sampled-data control | Conservatism | Semidefinite programming | Robust linear matrix inequality | Asymptotic exactness | Adaptive division | RELAXATIONS | DELAY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Control systems | Analysis | Intervals | Stability | Stabilization | Stability analysis | Tightness | Linear matrix inequalities | Sampling

Journal Article

Neural Networks, ISSN 0893-6080, 05/2016, Volume 77, pp. 80 - 86

.... Using a new proposed inequality called free-matrix-based integral inequality, a less conservative criterion is proposed, which is expressed by linear matrix inequalities...

Exponential stability | Neural networks | Time-varying delay | Lyapunovâ€“Krasovskii functional | Lyapunov-Krasovskii functional | SYSTEMS | ASYMPTOTIC STABILITY | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Neural Networks (Computer) | Equality | Electrical engineering | Information science | Stability | Integrals | Inequalities | Criteria | Linear matrix inequalities | Delay

Exponential stability | Neural networks | Time-varying delay | Lyapunovâ€“Krasovskii functional | Lyapunov-Krasovskii functional | SYSTEMS | ASYMPTOTIC STABILITY | NEUROSCIENCES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms | Neural Networks (Computer) | Equality | Electrical engineering | Information science | Stability | Integrals | Inequalities | Criteria | Linear matrix inequalities | Delay

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 07/2015, Volume 39, Issue 14, pp. 4151 - 4163

A matrix iteration algorithm was proposed by Peng (2012) for solving unconstrained matrix inequality AXB...

Least squares subproblem | Matrix inequality | Krylov subspace | Matrix-form LSQR method | Linear constraints | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EQUATION AXB | ENGINEERING, MULTIDISCIPLINARY | LSQR | ALGORITHMS | Algorithms | Equality | Analysis | Methods

Least squares subproblem | Matrix inequality | Krylov subspace | Matrix-form LSQR method | Linear constraints | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EQUATION AXB | ENGINEERING, MULTIDISCIPLINARY | LSQR | ALGORITHMS | Algorithms | Equality | Analysis | Methods

Journal Article

Automatica (Oxford), ISSN 0005-1098, 2001, Volume 37, Issue 9, pp. 1407 - 1416

.... The main contribution of the paper is that the AWBT controller synthesis, using static compensation, is cast as a convex optimization over linear matrix inequalities.

Passivity theorem | Input nonlinearity | Linear matrix inequality | Constrained system | Bumpless transfer | Absolute stability | Anti-windup | Multiplier theory | multiplier theory | passivity theorem | FEEDBACK SYSTEMS | NONLINEARITIES | absolute stability | linear matrix inequality | ENGINEERING, ELECTRICAL & ELECTRONIC | input nonlinearity | constrained system | anti-windup | CONTROL-SYSTEMS | INPUT-OUTPUT STABILITY | SATURATION | AUTOMATION & CONTROL SYSTEMS | bumpless transfer

Passivity theorem | Input nonlinearity | Linear matrix inequality | Constrained system | Bumpless transfer | Absolute stability | Anti-windup | Multiplier theory | multiplier theory | passivity theorem | FEEDBACK SYSTEMS | NONLINEARITIES | absolute stability | linear matrix inequality | ENGINEERING, ELECTRICAL & ELECTRONIC | input nonlinearity | constrained system | anti-windup | CONTROL-SYSTEMS | INPUT-OUTPUT STABILITY | SATURATION | AUTOMATION & CONTROL SYSTEMS | bumpless transfer

Journal Article

16.
Full Text
Fast Robust Nanopositioning-A Linear-Matrix-Inequalities-Based Optimal Control Approach

IEEE/ASME Transactions on Mechatronics, ISSN 1083-4435, 08/2009, Volume 14, Issue 4, pp. 414 - 422

.... The main theoretical contribution of this paper is the formulation of a multiobjective 2-DOF optimal control problem in terms of linear matrix inequalities, which are then solved using standard...

Atomic measurements | Atomic force microscopy | Uncertainty | Nanopositioning | 2-DOF control design | Nanobioscience | Robust control | High bandwidth | robust nanopositioning | Optimal control | Bandwidth | linear matrix inequalities (LMIs) | Probes | Hysteresis | high resolution | High resolution | Linear matrix inequalities (LMIs) | Robust nanopositioning | CONTROL DESIGN | HYSTERESIS | ENGINEERING, MANUFACTURING | FEEDBACK | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, MECHANICAL | ENGINEERING, ELECTRICAL & ELECTRONIC

Atomic measurements | Atomic force microscopy | Uncertainty | Nanopositioning | 2-DOF control design | Nanobioscience | Robust control | High bandwidth | robust nanopositioning | Optimal control | Bandwidth | linear matrix inequalities (LMIs) | Probes | Hysteresis | high resolution | High resolution | Linear matrix inequalities (LMIs) | Robust nanopositioning | CONTROL DESIGN | HYSTERESIS | ENGINEERING, MANUFACTURING | FEEDBACK | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, MECHANICAL | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

IEEE transactions on fuzzy systems, ISSN 1063-6706, 2001, Volume 9, Issue 2, pp. 324 - 332

This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems...

Linear systems | Fuzzy control | Instruction sets | Control system synthesis | Control systems | Numerical simulation | Linear matrix inequalities | Helium | Nonlinear systems | Fuzzy systems | Parameterized linear matrix inequality (PLMI) | LMIS | parameterized linear matrix inequality (PLMI) | UNCERTAIN SYSTEMS | fuzzy systems | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Design engineering | Systems design | Computer simulation | Mathematical models

Linear systems | Fuzzy control | Instruction sets | Control system synthesis | Control systems | Numerical simulation | Linear matrix inequalities | Helium | Nonlinear systems | Fuzzy systems | Parameterized linear matrix inequality (PLMI) | LMIS | parameterized linear matrix inequality (PLMI) | UNCERTAIN SYSTEMS | fuzzy systems | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Design engineering | Systems design | Computer simulation | Mathematical models

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 06/2012, Volume 57, Issue 6, pp. 1456 - 1467

Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modeled by parametrized polynomial matrix inequalities (PMIs...

Symmetric matrices | polynomial matrix inequality | robust optimization | Linear matrix inequalities | Approximation methods | Optimization | positive polynomials | moments | robust fixed-order controller design | Stability criteria | Polynomials | Linear matrix inequality (LMI) | Numerical stability | RELAXATIONS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Technology application | Usage | Analysis | Control systems | Design and construction | Hessian matrices | Mathematical optimization | Studies | Approximation | Hierarchies | Stability | Asymptotic properties | Inequalities | Mathematical models | Convergence | Mathematics | Optimization and Control

Symmetric matrices | polynomial matrix inequality | robust optimization | Linear matrix inequalities | Approximation methods | Optimization | positive polynomials | moments | robust fixed-order controller design | Stability criteria | Polynomials | Linear matrix inequality (LMI) | Numerical stability | RELAXATIONS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Technology application | Usage | Analysis | Control systems | Design and construction | Hessian matrices | Mathematical optimization | Studies | Approximation | Hierarchies | Stability | Asymptotic properties | Inequalities | Mathematical models | Convergence | Mathematics | Optimization and Control

Journal Article

IEEE transactions on information theory, ISSN 1557-9654, 2019, Volume 65, Issue 8, pp. 5239 - 5242

Consider a linear space L of complex D...

Symmetric matrices | Stationary state | Two dimensional displays | Mathematics | algebra | Linear matrix inequalities | Matrix decomposition | matrices | linear algebra | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Symmetric matrices | Stationary state | Two dimensional displays | Mathematics | algebra | Linear matrix inequalities | Matrix decomposition | matrices | linear algebra | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Automatica (Oxford), ISSN 0005-1098, 2013, Volume 49, Issue 9, pp. 2860 - 2866

... expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability...

Time-delay systems | Stability analysis | Sampled-data systems | Jensen inequality | LINEAR-SYSTEMS | INTERVAL | CRITERIA | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | DEPENDENT STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Workshops (Educational programs) | Equality | Stability | Integrals | Inequalities | Tools | Fourier analysis | Linear matrix inequalities | Gain | Engineering Sciences | Automatic

Time-delay systems | Stability analysis | Sampled-data systems | Jensen inequality | LINEAR-SYSTEMS | INTERVAL | CRITERIA | STABILIZATION | AUTOMATION & CONTROL SYSTEMS | DEPENDENT STABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | Workshops (Educational programs) | Equality | Stability | Integrals | Inequalities | Tools | Fourier analysis | Linear matrix inequalities | Gain | Engineering Sciences | Automatic

Journal Article

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