Robust Control of Switched Linear Systems with Output Switching Strategy
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Robust Control of Switched Linear Systems with Output Switching Strategy Edson Italo Mainardi Júnior1 · Marcelo Carvalho Minhoto Teixeira3 · Rodrigo Cardim3 · Edvaldo Assunção3 · Manoel Rodrigo Moreira3 · Diogo Ramalho de Oliveira3 · Alexandre Ataide Carniato2
Received: 19 December 2014 / Revised: 29 May 2015 / Accepted: 19 June 2015 / Published online: 7 July 2015 © Brazilian Society for Automatics–SBA 2015
Abstract This paper investigates the robust control problem of continuous-time uncertain switched linear systems, using only a switching strategy depending on the plant output. The proposed method is based on linear matrix inequalities (LMIs). A set of slack variables is introduced to reduce the design conservatism, and new sufficient LMI conditions for the synthesis of the controllers are presented. Two examples show that the proposed method has an adequate performance even in situations when the matrices of the linear subsystems
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Edson Italo Mainardi Júnior [email protected] Marcelo Carvalho Minhoto Teixeira [email protected] Rodrigo Cardim [email protected] Edvaldo Assunção [email protected] Manoel Rodrigo Moreira [email protected] Diogo Ramalho de Oliveira [email protected] Alexandre Ataide Carniato [email protected]
1
Instituto Federal de Educação, Ciência e Tecnologia Catarinense (IFC), Campus Videira, Rodovia SC 135, Videira, SC 89560-000, Brazil
2
Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP), Campus Presidente Epitácio, Av José Ramos Júnior, 27-50, Presidente Epitácio, SP 19470-000, Brazil
3
Laboratório de Pesquisa em Controle (LPC), Departamento de Engenharia Elétrica, Faculdade de Engenharia, Univ Estadual Paulista (UNESP), Campus Ilha Solteira, Avenida José Carlos Rossi, 1370, Ilha Solteira, SP 15385-000, Brazil
are not Hurwitz and offers a simple and efficient solution for this control problem. Keywords Switched linear systems · Quadratic Lyapunov function · Output switching strategy · Linear matrix inequalities · Robust control with polytopic uncertainties
1 Introduction In recent decades, the scientific community has shown a growing interest in the study of the stability of switched linear systems (Geromel and Colaneri 2006; Zhai et al. 2003). This interest is mainly due to the fact that they usually allow a better overall performance, namely their applications in practical systems such as: mechanical control systems, process control, power systems, aircraft control, automotive industry, power electronics (Yoshimura et al. 2013; Scharlau et al. 2014; Mainardi Júnior et al. 2012a; Cardim et al. 2009; Deaecto et al. 2010). In general, the theory of switched linear systems can be divided into two groups, where the first one occurs when the switching strategy σ (t) is independent of the system state variables and the second one occurs when σ (t) is a control variable dependent on the state variables of the system (Geromel and Colaneri 2006). The main goal of this paper is to design an appropriate output switching
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