Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function
Asier Ibeas,Manuel De la Sen +1 more
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TLDR
In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices, obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching and calculating an upper bound for the output during its transient response.About:
This article is published in Applied Mathematics Letters.The article was published on 2009-10-01 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Exponential stability & Lyapunov function.read more
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Stabilization and L 2 -gain analysis for a class of cascade switched nonlinear systems: An average dwell-time method
TL;DR: In this paper, a state feedback controller and an average dwell-time scheme are designed to guarantee that the corresponding closed-loop system is globally asymptotically stable and has a weighted L 2 -gain.
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On robust Lie-algebraic stability conditions for switched linear systems
TL;DR: New sufficient conditions for exponential stability of switched linear systems under arbitrary switching are presented, which involve the commutators (Lie brackets) among the given matrices generating the switched system.
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Supervisory Fault Tolerant Control with Mutual Performance Optimization
TL;DR: In this paper, the problem of active fault-tolerant control with reconfiguration mechanism for uncertain linear systems with external disturbances is addressed applying the supervisory control approach, and a key feature of the proposed approach is establishment of a set of conditions providing mutual performance in the sense of taking into account the interaction of the fault detection, isolation, and accommodation subsystems.
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Event triggered control for a switched LPV system with applications to aircraft engines
Kongwei Zhu,Dan Ma,Jun Zhao +2 more
TL;DR: The event triggered control for a kind of switched linear parameter varying (LPV) systems is studied and two event triggering schemes are given, depending on whether the controllers are pre-designed or to be designed.
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Finding common quadratic Lyapunov functions for switched linear systems using particle swarm optimisation
TL;DR: A new methodology for calculating a common quadratic Lyapunov function (CQLF) based on particle swarm optimisation (PSO) once the existence of a CQLF has been assured.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
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Basic problems in stability and design of switched systems
Daniel Liberzon,A.S. Morse +1 more
TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
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Stability of switched systems: a Lie-algebraic condition
TL;DR: In this article, a sucient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices is presented, and it is shown that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function.
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Lie-Algebraic Stability Criteria for Switched Systems
TL;DR: It is demonstrated that if a Lie algebra fails to satisfy the above condition, then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable.
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A result on common quadratic Lyapunov functions
TL;DR: This note defines strong and weak common quadratic Lyapunov functions (CQLFs) for sets of linear time-invariant (LTI) systems and shows that the simultaneous existence of a weak CQLF of a special form, and the nonexistence of a strong CQLFs, for a pair of LTI systems is characterized by easily verifiable algebraic conditions.
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Hai Lin,Panos J. Antsaklis +1 more