Robust stabilization and ℋ∞ control by means of state-feedback for polytopic linear systems using LMIs and scalar searches

Author

Vieira, Henrique S. ; Oliveira, Ricardo C. L. F. ; Peres, Pedro L. D.

Author_Institution

Sch. of Electr. & Comput. Eng., Univ. of Campinas - UNICAMP, Campinas, Brazil

fYear

2015

fDate

1-3 July 2015

Firstpage

5966

Lastpage

5973

Abstract

The problems of robust stabilization and robust ℋ_∞ control by means of state feedback for uncertain linear systems in polytopic domains are investigated in this paper. New synthesis conditions based on LMI relaxations and search of scalar variables are proposed for both continuous and discrete-time systems. The main novelty comes from the fact that the closed-loop stability is certified by means of polynomially parameter-dependent Lyapunov matrices. It is also shown that the proposed conditions contain as particular cases the less conservative conditions available in the literature for this class of systems. Numerical experiments illustrate the efficiency of the proposed relaxations.

Keywords

H^∞ control; Lyapunov matrix equations; closed loop systems; discrete time systems; linear matrix inequalities; linear systems; robust control; state feedback; uncertain systems; LMI relaxation; closed-loop stability; discrete-time system; polynomially parameter-dependent Lyapunov matrix; polytopic domain; polytopic linear system; robust ℋ∞ control; robust stabilization; scalar search; state feedback; state-feedback; synthesis condition; uncertain linear system; Closed loop systems; Databases; Discrete-time systems; Linear matrix inequalities; Linear systems; Polynomials; Robustness;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference (ACC), 2015

Conference_Location

Chicago, IL

Print_ISBN

978-1-4799-8685-9

Type

conf

DOI

10.1109/ACC.2015.7172276

Filename

7172276