LMI relaxations for non-quadratic discrete stabilization via Pólya Theorem

Author

Lo, Ji-Chang ; Tsai, Chin-Fu

Author_Institution

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

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

7430

Lastpage

7435

Abstract

In this paper, a relaxation technique based on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs) is proposed. We investigate non-quadratic relaxed conditions characterized by parameter-dependent LMIs (PD-LMIs) in terms of parameter uncertainty belonging to the unit simplex, exploiting the algebraic property of Polya´s Theorem to construct a family of finite-dimensional LMI relaxations that releases conservatism. Lastly, a numerical experiment to illustrate the advantage of relaxation, being less conservative and reaching exactness, are provided.

Keywords

discrete time systems; linear matrix inequalities; stability; LMI relaxations; Polya theorem; homogeneous polynomially parameter-dependent solutions; linear matrix inequalities; nonquadratic discrete stabilization; parameter uncertainty; parameter-dependent LMIs; Homogeneous Polynomials; Linear matrix inequality (LMI); Parameter-dependent LMIs (PD-LMIs); Relaxation;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5399994

Filename

5399994