On the Analysis of Systems Described by Classes of Partial Differential Equations

Author

Papachristodoulou, Antonis ; Peet, Matthew Monnig

Author_Institution

Dept. of Eng. Sci., Oxford Univ.

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

747

Lastpage

752

Abstract

We provide an algorithmic approach for the analysis of infinite dimensional systems described by partial differential equations. In particular, we look at the stability properties of a class of strongly continuous semigroups generated by nonlinear parabolic partial differential equations with appropriate boundary conditions. Our approach is based on the application of semidefinite programming to the computation of Lyapunov-type certificates defined by polynomial functions. An illustrative example is given

Keywords

Lyapunov methods; control system analysis; distributed parameter systems; mathematical programming; multidimensional systems; nonlinear differential equations; parabolic equations; partial differential equations; polynomials; stability; Lyapunov-type certificates; infinite dimensional systems; nonlinear parabolic equations; partial differential equations; polynomial functions; semidefinite programming; stability; strongly continuous semigroups; Algorithm design and analysis; Boundary conditions; Control systems; Numerical simulation; Partial differential equations; Polynomials; Robust stability; Space heating; Stability analysis; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377815

Filename

4177885