Stabilization criteria of a class of switched systems

Abstract

In this paper, stabilizability property for a switched system under arbitrary switching is considered from an algebraic point of view by means of the existence of a set of block‐diagonal Lyapunov solutions with common Schur complement of certain order—or, equivalently, with common block (1,1)—for the matrix bank. It is shown that the existence of that set is equivalent to the existence of solutions for some Riccati inequalities done in terms of the blocks of matrices of the bank. In addition, we conclude that a particular class of systems with matrix bank constituted by Metzler matrices—Positive Switched Systems—are stabilizable by partial state reset.

An approach to the stability of reset switched systems using dynamics without reset

“…Since the switching rules are arbitrary, the associated invariant systems must be stable. A similar framework was used in [10,15,16], where the possibility of stabilizing the switched systems by resetting only a part of the state components, with some adequate choice of resets, was studied. Recently, other authors have considered similar stabilization problems in different frameworks; see, for instance, [17][18][19].…”