Brief paper: Root-mean-square gains of switched linear systems: A variational approach
Automatica (Journal of IFAC)
Brief paper: Simultaneous Schur stability of interval matrices
Automatica (Journal of IFAC)
Brief paper: Growth rate of switched homogeneous systems
Automatica (Journal of IFAC)
Brief paper: On linear co-positive Lyapunov functions for sets of linear positive systems
Automatica (Journal of IFAC)
Signal reconstruction over switching channels: a model matching approach
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
Brief paper: Periodic stabilizability of switched linear control systems
Automatica (Journal of IFAC)
International Journal of Systems Science
Exponential stabilization of discrete-time switched linear systems
Automatica (Journal of IFAC)
Brief paper: A control design method for a class of switched linear systems
Automatica (Journal of IFAC)
A convex optimization approach to signal reconstruction over switching networks
Automatica (Journal of IFAC)
State-feedback stabilizability in switched homogeneous systems
ACC'09 Proceedings of the 2009 conference on American Control Conference
A generating function approach to the stability of discrete-time switched linear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Stabilization of planar switched linear systems using polar coordinates
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Brief paper: On the algebraic characterization of invariant sets of switched linear systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Brief paper: Componentwise ultimate bound and invariant set computation for switched linear systems
Automatica (Journal of IFAC)
Polynomial-Time Computation of the Joint Spectral Radius for Some Sets of Nonnegative Matrices
SIAM Journal on Matrix Analysis and Applications
Criteria of Stability for Continuous-Time Switched Systems by Using Liao-Type Exponents
SIAM Journal on Control and Optimization
On the Stabilization of Persistently Excited Linear Systems
SIAM Journal on Control and Optimization
Input-to-state stability of impulsive and switching hybrid systems with time-delay
Automatica (Journal of IFAC)
Stability and stabilization of mechanical systems with switching
Automation and Remote Control
Analysis of hybrid systems' dynamics using the common Lyapunov functions and multiple homomorphisms
Automation and Remote Control
Brief paper: Dynamic output feedback H∞ control of switched linear systems
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Stability analysis for a class of switched nonlinear systems
Automatica (Journal of IFAC)
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces
SIAM Journal on Control and Optimization
Analysis of Discrete-Time Linear Switched Systems: A Variational Approach
SIAM Journal on Control and Optimization
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Stability analysis of impulsive switched systems with time delays
Mathematical and Computer Modelling: An International Journal
Some results on the stabilization of switched systems
Automatica (Journal of IFAC)
Computation of joint spectral radius for network model associated with rank-one matrix set
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Automatica (Journal of IFAC)
Limited-information control of hybrid systems via reachable set propagation
Proceedings of the 16th international conference on Hybrid systems: computation and control
On dimensionality reduction and the stability of a class of switched descriptor systems
Automatica (Journal of IFAC)
Stability of fractional order switching systems
Computers & Mathematics with Applications
Exponential stability of stochastic systems with hysteresis switching
Automatica (Journal of IFAC)
Finite data-rate feedback stabilization of switched and hybrid linear systems
Automatica (Journal of IFAC)
An experimental study of approximation algorithms for the joint spectral radius
Numerical Algorithms
Hi-index | 0.05 |
The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving them in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability and also represent problems in which significant progress has been made. We also comment on the inherent difficulty in determining stability of switched systems in general, which is exemplified by NP-hardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems are reviewed. We briefly comment on the classical Lur'e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.