Robust stability and stabilization studies for uncertain switched systems based on vector norms approach

Abstract

In this paper, we investigate the problems of robust stability and stabilization via a state feedback controller for both continuous and discrete-time switched linear systems with polytopic uncertainties. These considered systems are represented in the state form. Then, a transformation under the arrow form is performed. Thus, based on the construction of a common Lyapunov function associated with the application of the Kotelyanski lemma, the M-matrix proprieties and the aggregation techniques, new sufficient conditions for robust stability and stabilization under arbitrary switching laws are established. It should be pointed out that the obtained results are explicit, easy to apply and formulated in terms of the polytopic uncertainty parameters. In addition, this proposed method allows us to avoid the search of a common Lyapunov function which is a difficult matter. For illustration, a DC motor model with separate excitation under variable mechanical loads is used to show the effectiveness and the potential of the proposed techniques.

Simple Algebraic Criteria for Asymptotic Stability of a Class of TS Fuzzy Time-Delay Switched Systems

“…The first one is based on searching sufficient conditions guaranteeing the asymptotic stability of such systems under an arbitrary switching law [12,13]. This kind of switching, which is the subject of this paper, is also called random or unconstrained switching.…”

Delay‐Dependent Stability Analysis of TS Fuzzy Switched Time‐Delay Systems

“…Nevertheless, the simplicity of vector norms based approach makes the study almost feasible in most cases in Example 3 (see [38,45]). Consider a DC motor with separate excitation (Figure 9).…”

“…The application of vector norms to switched systems has already been introduced in [44][45][46][47]. It has been extended later to switched time-delay systems in [48][49][50][51][52][53].…”