IEEE Transactions on Automatic Control, ISSN 0018-9286, 10/2015, 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...

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

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

Book

IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2011, Volume 56, Issue 7, pp. 1660 - 1665

The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Grüss...

Symmetric matrices | Conservatism | Grüss inequality | Linear matrix inequalities | Delay | fragmentation | sampled-data systems | Convergence | Upper bound | Jensen's inequality | time-delay systems | Integral equations | Convex functions | Gruss inequality | STABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Electronic data processing | Usage | Numerical analysis | Innovations | Delay lines | Methods | Nonuniform | Equivalence | Partitioning | Inequalities | Automatic control | Empirical analysis | Fragmentation | Computational Mathematics | Optimeringslära, systemteori | Mathematics | Optimization, systems theory | Tillämpad matematik | Naturvetenskap | Applied mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Symmetric matrices | Conservatism | Grüss inequality | Linear matrix inequalities | Delay | fragmentation | sampled-data systems | Convergence | Upper bound | Jensen's inequality | time-delay systems | Integral equations | Convex functions | Gruss inequality | STABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Electronic data processing | Usage | Numerical analysis | Innovations | Delay lines | Methods | Nonuniform | Equivalence | Partitioning | Inequalities | Automatic control | Empirical analysis | Fragmentation | Computational Mathematics | Optimeringslära, systemteori | Mathematics | Optimization, systems theory | Tillämpad matematik | Naturvetenskap | Applied mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 01/2019, Volume 34, Issue 1, pp. 62 - 78

This document describes our freely distributed Maple library spectra, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It...

semidefinite programming | computer algebra | symbolic computation | real algebraic geometry | linear matrix inequalities | low rank matrices | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SQUARES | SUMS | Software | Linear matrix inequalities | Mathematical analysis | Matrix methods | Arithmetic | Mathematical programming | Algebraic Geometry | Mathematics | Optimization and Control | Symbolic Computation | Computer Science

semidefinite programming | computer algebra | symbolic computation | real algebraic geometry | linear matrix inequalities | low rank matrices | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SQUARES | SUMS | Software | Linear matrix inequalities | Mathematical analysis | Matrix methods | Arithmetic | Mathematical programming | Algebraic Geometry | Mathematics | Optimization and Control | Symbolic Computation | Computer Science

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⩾C, and it can be amplified to solve the matrix...

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

IEEE Transactions on Fuzzy Systems, ISSN 1063-6706, 04/2001, Volume 9, Issue 2, pp. 324 - 332

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

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

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

This paper is concerned with global exponential stability problem for a class of neural networks with time-varying delays. Using a new proposed inequality...

Exponential stability | Neural networks | Time-varying delay | Lyapunov–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 | Lyapunov–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

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...

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

Automatica, ISSN 0005-1098, 09/2013, Volume 49, Issue 9, pp. 2860 - 2866

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to...

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

Applied Mathematics and Computation, ISSN 0096-3003, 05/2015, Volume 259, pp. 327 - 338

In this paper, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online time-varying linear...

ZNN design formula | Zhang neural network (ZNN) | Time-varying | Conversion | Linear matrix–vector inequality (LMVI) | Linear matrix-vector inequality (LMVI) | MATHEMATICS, APPLIED | DYNAMIC-SYSTEM | EQUATIONS | ALGORITHMS | RESOLVING MANIPULATOR REDUNDANCY | ZHANG NEURAL-NETWORK | VARIANT | OBSTACLE-AVOIDANCE | Analysis | Equality

ZNN design formula | Zhang neural network (ZNN) | Time-varying | Conversion | Linear matrix–vector inequality (LMVI) | Linear matrix-vector inequality (LMVI) | MATHEMATICS, APPLIED | DYNAMIC-SYSTEM | EQUATIONS | ALGORITHMS | RESOLVING MANIPULATOR REDUNDANCY | ZHANG NEURAL-NETWORK | VARIANT | OBSTACLE-AVOIDANCE | Analysis | Equality

Journal Article

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

Let A(x) = A(0)+x(1)A(1)+...+x(n)A(n) be a linear matrix, or pencil, generated by given symmetric matrices A(0), A(1,)...,A(n) of size m with rational entries....

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

Applied Mathematics and Computation, ISSN 0096-3003, 08/2019, Volume 354, pp. 1 - 8

This paper focuses on the delay-dependent stability problem of time-varying delay systems. A generalized free-matrix-based integral inequality (GFMBII) is...

Linear matrix inequality | Free-matrix-based integral inequality(FMBII) | Stability | Time-varying delay | LINEAR-SYSTEMS | CRITERIA | SYNCHRONIZATION | MATHEMATICS, APPLIED | STABILIZATION | LURE SYSTEMS | Equality

Linear matrix inequality | Free-matrix-based integral inequality(FMBII) | Stability | Time-varying delay | LINEAR-SYSTEMS | CRITERIA | SYNCHRONIZATION | MATHEMATICS, APPLIED | STABILIZATION | LURE SYSTEMS | Equality

Journal Article

13.
Full Text
A survey of linear matrix inequality techniques in stability analysis of delay systems

International Journal of Systems Science, ISSN 0020-7721, 12/2008, Volume 39, Issue 12, pp. 1095 - 1113

Recent years have witnessed a resurgence of research interests in analysing the stability of time-delay systems. Many results have been reported using a...

delay-dependent stability | time-delay systems | delay-independent stability | linear matrix inequality | Time-delay systems | Linear matrix inequality | Delay-independent stability | Delay-dependent stability | DEPENDENT ROBUST STABILITY | GUARANTEED COST CONTROL | DISCRETE-TIME-SYSTEMS | VARYING DELAY | UNCERTAIN NEUTRAL SYSTEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | S FUZZY-SYSTEMS | H-INFINITY-CONTROL | LARGE-SCALE SYSTEMS | LYAPUNOV-KRASOVSKII FUNCTIONALS | OUTPUT-FEEDBACK STABILIZATION | COMPUTER SCIENCE, THEORY & METHODS | AUTOMATION & CONTROL SYSTEMS

delay-dependent stability | time-delay systems | delay-independent stability | linear matrix inequality | Time-delay systems | Linear matrix inequality | Delay-independent stability | Delay-dependent stability | DEPENDENT ROBUST STABILITY | GUARANTEED COST CONTROL | DISCRETE-TIME-SYSTEMS | VARYING DELAY | UNCERTAIN NEUTRAL SYSTEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | S FUZZY-SYSTEMS | H-INFINITY-CONTROL | LARGE-SCALE SYSTEMS | LYAPUNOV-KRASOVSKII FUNCTIONALS | OUTPUT-FEEDBACK STABILIZATION | COMPUTER SCIENCE, THEORY & METHODS | AUTOMATION & CONTROL SYSTEMS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2019, 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, ISSN 0005-1098, 02/2019, Volume 100, pp. 289 - 298

This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞...

Sampled-data control | Linear systems | LMI | Optimal control | STABILIZATION | PERFORMANCE | CONVEX CONDITIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DATA SYSTEMS | STABILITY ANALYSIS | GENERAL FRAMEWORK | FEEDBACK | AUTOMATION & CONTROL SYSTEMS

Sampled-data control | Linear systems | LMI | Optimal control | STABILIZATION | PERFORMANCE | CONVEX CONDITIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | DATA SYSTEMS | STABILITY ANALYSIS | GENERAL FRAMEWORK | FEEDBACK | AUTOMATION & CONTROL SYSTEMS

Journal Article

2011, 1, Princeton series in applied mathematics, ISBN 9780691121574, xv, 248

"Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the...

Non-negative matrices | Mathematics | Math

Non-negative matrices | Mathematics | Math

Book

IEEE Transactions on Automatic Control, ISSN 0018-9286, 05/2009, 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 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

Applied Mathematics and Computation, ISSN 0096-3003, 03/2018, Volume 321, pp. 37 - 48

This paper discusses the range of the eigenvalues of a class of matrices. By using the eigenvalues range of a class of matrices, an extension of the inner...

Principal angle | Eigenvalue | Cauchy–Schwarz inequality | Coupled Sylvester matrix equations | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | COMPLEX CONJUGATE | Cauchy-Schwarz inequality | PRODUCT | EQUATIONS | STATE | PARAMETER-ESTIMATION ALGORITHM | Methods | Algorithms | Equality

Principal angle | Eigenvalue | Cauchy–Schwarz inequality | Coupled Sylvester matrix equations | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | COMPLEX CONJUGATE | Cauchy-Schwarz inequality | PRODUCT | EQUATIONS | STATE | PARAMETER-ESTIMATION ALGORITHM | Methods | Algorithms | Equality

Journal Article