H2 and H∞ control of time-varying delay switched linear systems with application to sampled-data control. (November 2016)

• Record Type: Journal Article
• Authors: Deaecto, Grace S.; Bolzern, Paolo; Galbusera, Luca; Geromel, José C.
• Is Part Of: Nonlinear analysis. Volume 22(2016)
• Page Start: 43
• Page End: 54
• Publication Date: 2016-11
• Subjects: Switched systems -- Time-varying delay -- Sampled-data control -- LMI; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.03.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper deals with switched linear systems subject to time-varying delay. The main goal is to design state and output feedback switching strategies preserving closed-loop stability and a guaranteed H 2 or H ∞ performance. The switching strategies are based on a generalization of a recent extended version of the small gain theorem and do not require any assumption on the continuity of the delay and its time-variation rate. The key point to obtain the design conditions is the adoption of an equivalent switched linear system where the time-varying delay is modeled as a norm-bounded perturbation. Moreover, with this approach, it is possible to deal with sampled-data control systems. All conditions are formulated in terms of Lyapunov–Metzler inequalities, which allow the maximization of an upper bound on the time-delay preserving stability and guaranteed performance. Numerical examples are discussed in order to illustrate the effectiveness of the design approach.