Semi-definite programming and functional inequalities for distributed parameter systems

Author

Valmorbida, Giorgio ; Ahmadi, Mohamadreza ; Papachristodoulou, Antonis

Author_Institution

Dept. of Eng. Sci., Univ. of Oxford, Oxford, UK

fYear

2014

fDate

15-17 Dec. 2014

Firstpage

4304

Lastpage

4309

Abstract

We study one-dimensional integral inequalities on bounded domains, with quadratic integrands. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration. For the case of polynomial function matrices, sufficient conditions for positivity of the matrix inequality and, therefore, for the integral inequalities are cast as semi-definite programs. The inequalities are used to study stability of linear partial differential equations.

Keywords

distributed parameter systems; integration; linear differential equations; mathematical programming; matrix algebra; partial differential equations; polynomials; stability; bounded domains; distributed parameter systems; function matrix inequalities; integration; linear partial differential equations; one-dimensional integral inequalities; polynomial function matrices; quadratic integrands; semidefinite programming; stability; sufficient conditions; Linear matrix inequalities; Lyapunov methods; Numerical stability; Polynomials; Stability analysis; Vectors; Distributed Parameter Systems; PDEs; Stability Analysis; Sum of Squares;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on

Conference_Location

Los Angeles, CA

Print_ISBN

978-1-4799-7746-8

Type

conf

DOI

10.1109/CDC.2014.7040060

Filename

7040060