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2014, Graduate studies in mathematics, ISBN 0821883194, Volume 158, xv, 284
Book
1988, ISBN 3540192492, Volume 1313., vi, 177
Book
2000, Systems & control., ISBN 3764336838, xii, 629
Book
Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 05/2018, Volume 38, Issue 3, pp. 921 - 939
Two notions of metric invariance entropy are constructed with respect to conditionally invariant measures for control systems in discrete time and it is shown... 
MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR STABILIZATION | TOPOLOGICAL FEEDBACK ENTROPY | SETS | Entropy | Invariance | Discrete time systems | Invariants
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 04/2018, Volume 38, Issue 4, pp. 2093 - 2123
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a... 
Transitivity set | Quasi-stationary measures | Control sets | Codercontrollers | Invariance entropy | MATHEMATICS | MATHEMATICS, APPLIED | coder-controllers | TRANSITIVITY | transitivity set | quasi-stationary measures | control sets | DISCRETE-TIME-SYSTEMS
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2012, Volume 50, Issue 5, pp. 2988 - 3010
Minimal bit rates and entropy are studied for exponential stabilization of control systems in continuous time. Upper and lower bounds for the stabilization... 
Stabilization entropy | Minimal bit rates | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | stabilization entropy | INVARIANCE ENTROPY | minimal bit rates | CONSTRAINTS | FEEDBACK | AUTOMATION & CONTROL SYSTEMS
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2019, Volume 11539, pp. 178 - 191
Conference Proceeding
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2009, Volume 48, Issue 3, pp. 1701 - 1721
For continuous time control systems, this paper introduces invariance entropy as a measure for the amount of information necessary to achieve invariance of... 
Invariant covering | Invariance | Topological entropy | Nonlinear control | LINEAR-SYSTEMS | topological entropy | MATHEMATICS, APPLIED | nonlinear control | COMMUNICATION BANDWIDTH CONSTRAINTS | STABILIZATION | invariance | DATA RATES | invariant covering | FEEDBACK | STABILIZABILITY | AUTOMATION & CONTROL SYSTEMS | Studies | Control systems | Entropy | Nonlinear systems | Eigen values
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2019
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2016, Volume 289, Issue 16, pp. 1995 - 2006
Journal Article
Procedia IUTAM, ISSN 2210-9838, 2013, Volume 6, pp. 151 - 159
For random diffeomorphisms the relation between conditionally stationary measures and controllability properties of an associated deterministic control system... 
Random diffeomorphisms | Control sets | Conditional stationarity
Journal Article
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 04/2014, Volume 94, Issue 4, pp. 276 - 276
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2016, Volume 289, Issue 16, pp. 1995 - 2006
Topological conjugacy for continuous skew product flows on topological group bundles and semidirect products is studied resulting in a splitting theorem. The... 
Topological conjugacy | Lind's functional equation | skew product flows | 93B99 | 22F05 | fiber entropy | 37B55 | 37B05 | MATHEMATICS
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 3/2019, Volume 31, Issue 1, pp. 1 - 23
Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance... 
Ordinary Differential Equations | Feedbacks | Control systems | Mathematics | Applications of Mathematics | Invariance pressure | Invariant covers | Invariance entropy | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Optimization and Control
Journal Article
Systems & Control Letters, ISSN 0167-6911, 05/2013, Volume 62, Issue 5, pp. 377 - 381
For discrete-time control systems, notions of entropy for invariance are compared. One is based on feedbacks, and the other one on open-loop control functions.... 
Topological feedback entropy | Invariance entropy | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | AUTOMATION & CONTROL SYSTEMS | Control systems
Journal Article
Mathematical Control and Related Fields, ISSN 2156-8472, 2018, Volume 8, Issue 1, pp. 39 - 58
Journal Article
Systems & Control Letters, ISSN 0167-6911, 05/2013, Volume 62, Issue 5, pp. 377 - 381
For discrete-time control systems, notions of entropy for invariance are compared. One is based on feedbacks, and the other one on open-loop control functions.... 
Equivalence | Feedback | Control systems | Entropy | Topology | Control theory | Invariance
Journal Article
Nonlinearity, ISSN 0951-7715, 08/2017, Volume 30, Issue 9, pp. 3400 - 3418
For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of... 
piecewise deterministic Markov process | invariant measures | control sets | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | DYNAMICAL-SYSTEMS
Journal Article
IMA Journal of Mathematical Control and Information, ISSN 0265-0754, 09/2016, Volume 33, Issue 3, pp. 701 - 722
For non-linear systems described by ordinary differential equations, the paper studies W-control sets which are defined as maximal subsets of complete... 
invariance entropy | safe regions | control sets | MATHEMATICS, APPLIED | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENTROPY
Journal Article
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