Robust switched control based on strictly positive real systems and variable structure control techniques

Abstract

Summary This paper is concerned with the design of variable structure controllers for uncertain switched linear plants. The proposed method is based on Lyapunov–Metzler inequalities and on properties of strictly positive real (SPR) systems, with the advantage that it can be applied in control of uncertain switched linear system. The first contribution shows that there exists a solution of the SPR synthesis for a class of linear uncertain switched systems using switched static output feedback, if and only if there exists a solution of this SPR synthesis with switched static state feedback. This result is a generalization of known conditions regarding this problem, for linear time‐invariant and known (without uncertainties) plants, and offers a possible procedure for output feedback SPR synthesis: first solve the state feedback SPR synthesis and then, using the obtained solution, find a solution for the output feedback SPR synthesis. Next are presented necessary and sufficient (sufficient) conditions for the SPR synthesis for a class of linear uncertain switched systems using switched static output feedback, for plants with the same number of inputs and outputs (with the number of outputs greater than the number of inputs). Two examples illustrate the effectiveness of the robust control system, including applications of the proposed methods, considering switched static state feedback and switched static output feedback, in the design of switching control strategies for active suspensions systems in road vehicles. Performance indices such as decay rate, guaranteed cost, and restriction in the norm of controller gains are considered in these designs. Copyright © 2016 John Wiley & Sons, Ltd.

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

“…. α r ] represents the polytopic uncertainties of the plant or structural failures (Silva et al, 2013) and (Cardim et al, 2016). Consider that σ (t) ∈ K N is the switching strategy which selects at each instant of time an available subsystem i ∈ K N .…”

“…With the aim to compare the proposed technique with the results presented in Chang et al (2015) for continuous-time systems, the condition of Corollary 4.5 is used to cover the Example III. Finally, in Example IV the conditions of Theorem 4.3 are used in order to find a feasible solution for a practical application of the method in the design of a switched robust controller for a semi-active suspension (Cardim et al, 2016) and (Geromel et al, 2008) aiming to minimise the H ∞ cost (51). Concerning LMI solver, it was used the SeDuMi or Matlab LMI toolbox interfaced by YALMIP in MATLAB software.…”

“…The proposed procedure can also be used for designing robust controllers for uncertain plants subject to structural failures, considering the plant uncertainties and the structural failures as polytopic uncertainties (Silva, Assunção, Teixeira, & Cardim, 2013). An example illustrates a practical application of the method in the design and simulation of a robust controller of a semi-active suspension addressed in Cardim et al (2016) and Geromel, Colaneri, and Bolzern (2008). The paper is organised as follows.…”

“…Three examples in Section 6 illustrate the effectiveness of the proposed methods, including the design and simulation results of a robust controller of a semi-active suspension (Cardim et al, 2016) and showing that there exist cases where the proposed conditions hold and the conditions from Mainardi Júnior et al…”

From adaptive control to variable structure systems – seeking harmony

“…The paper by Cardim, Teixeira, Assunção, Ribeiro, Covacic, and Gainois concerns with the design of variable structure controllers for uncertain switched linear plants. The proposed method is based on Lyapunov–Metzler inequalities and on properties of strictly positive real (SPR) systems, with the advantage that it can be applied in control of uncertain switched linear system.…”