Robust Control of Switched Linear Systems with Output Switching Strategy

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

Output control of continuous-time uncertain switched linear systems via switched static output feedback

“…Figure 1 shows a comparison between the feasible regions obtained through the conditions of Theorems 3.2 and 3.3. Note that, the proposed methodology (Theorem 3.3) presents a greater feasible region than that obtained with the conditions given in (Theorem 5) (Mainardi Júnior et al, 2015). This fact and the result presented in Theorem 3.4 show that the conditions proposed in Theorem 3.3 are less conservative than that presented in Mainardi Júnior et al (2015).…”

“…In this example the condition regarding the guaranteed cost (7) is removed, adopting C 111 = C 112 = C 121 = C 122 = C 131 = C 132 = 0. Thus, note that the conditions from Theorem 3.2 are equivalent to the conditions presented on Theorem 5 (Mainardi Júnior et al, 2015). Figure 1 shows a comparison between the feasible regions obtained through the conditions of Theorems 3.2 and 3.3.…”

An LMI Approach to Full- and Reduced-Order Switched Luenberger Observers for Switched Affine Systems

“…Despite of the amount of research on SASs, there is no result on reducing the state estimator order, as far as the authors could search, which is an important feature in establishing observer-based control theory as already shown by Luenberger in his original works on Linear Systems (Luenberger 1964(Luenberger , 1971: it simplifies the observer implementation. Some helpful related insight can also be found in model reduction theory (Assunção et al 2007) and static output feedback (Mainardi Júnior et al 2015).…”

Estabilidade de sistemas chaveados descritores afins com aplica¸c˜ao em um circuito eletroestimulador

“…3 Logo, a contribuição principal deste artigo é a proposta de uma modelagem matemática e estudo de estabilidade de um circuito de estimulação elétrica para uma estratégia de chaveamento arbitrária. A análise de estabilidade foi reduzida a problemas descritos por LMIs (BOYD et al, 1994;CARNIATO et al, 2018;MAINARDI J ÚNIOR et al, 2015) que, quando factíveis, são facilmente resolvidos por meio de ferramentas disponíveis na literatura de programação convexa, por exemplo Gahinet et al (1995). Todavia, sistemas descritores chaveados não lineares afins são mais difíceis de serem controlados do que os sistemas chaveados lineares, pois é possível que os subsistemas não compartilhem o mesmo ponto de equilíbrio do sistema global.…”