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In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings. [ABSTRACT FROM PUBLISHER]

A sufficient condition for the stability of arbitrary switching linear systems (SLSs) without control inputs is that the individual subsystems are stable and their evolution matrices are simultaneously triangularizable (ST). This sufficient condition for stability is known to be extremely restrictive and not robust, and therefore of very limited applicability. The situation can be radically different when control inputs are present. Indeed, previous results have established that, depending on the number of states, inputs and subsystems, the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices are stable and ST can become a generic property, i.e., a property valid for almost every set of system parameters. This note provides novel contributions along two lines. First, we give sufficient conditions for the genericity of the property of existence of feedback matrices so that the subsystem closed-loop matrices are ST (not necessarily stable). Second, we give conditions for the genericity of the property of existence of feedback matrices that, in addition to achieving ST, enable arbitrary eigenvalue selection for each subsystem's closed-loop matrix. The latter conditions are less stringent than existing ones, and the approach employed in their derivation can be interpreted as an extension to SLSs of specific aspects of the notion of eigenvalue controllability for (non-switching) linear systems. [ABSTRACT FROM AUTHOR]

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques. [ABSTRACT FROM PUBLISHER]

In this paper, a unified framework is proposed to study the exponential stability of discrete-time switched linear systems and, more generally, the exponential growth rates of their trajectories under three types of switching rules: arbitrary switching, optimal switching, and random switching. It is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong, the weak, and the mean generating functions, respectively. In particular, necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence. Various properties of the generating functions are established, and their relations are discussed. Algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples. [ABSTRACT FROM AUTHOR]

This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter. [ABSTRACT FROM AUTHOR]

In this note, we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency. For both eases of known and unknown switching functions, feedback laws are designed to achieve exponential stability. For the later case, a method combining on-line adaptive estimation and feedback stabilization is developed in the controller design. [ABSTRACT FROM AUTHOR]