Existence of parameter-dependent Lyapunov functions assuring robust stability via SOS

Author

Lo, Ji-Chang ; Tsai, Chin-Fu

Author_Institution

Mech. Eng., Nat. Central Univ., Jhongli, Taiwan

fYear

2011

fDate

15-18 May 2011

Firstpage

1492

Lastpage

1497

Abstract

An SOS relaxation technique seeking homogeneous polynomially parameter dependent (HPPD) Lyapunov function to non-quadratic stability is proposed. We investigate non-quadratic relaxed conditions characterized by sum of squares, exploiting the algebraic property of Polya Theorem to construct a family of finite-dimensional SOS relaxations that releases conservatism without adding any slack matrices. Lastly, numerical experiments to illustrate the advantage of the relaxation, being simple and effective, are provided.

Keywords

Lyapunov methods; matrix algebra; multidimensional systems; relaxation theory; robust control; HPPD Lyapunov function; Polya theorem; SOS relaxation technique; algebraic property; finite-dimensional SOS relaxations; homogeneous polynomially parameter dependent Lyapunov function; nonquadratic relaxed conditions; nonquadratic stability; parameter-dependent Lyapunov functions; robust stability; slack matrices; sum of squares; Eigenvalues and eigenfunctions; Linear matrix inequalities; Lyapunov methods; Polynomials; Stability analysis; Symmetric matrices; Uncertain systems; Homogeneous polynomials; Linear matrix inequality; Non-common P; Parameter-dependent LMIs (PD-LMIs); Relaxation;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ASCC), 2011 8th Asian

Conference_Location

Kaohsiung

Print_ISBN

978-1-61284-487-9

Electronic_ISBN

978-89-956056-4-6

Type

conf

Filename

5899294