Title :
On parameter-dependent Lyapunov functions for robust stability of linear systems
Author :
Henrion, Didier ; Arzelier, Denis ; Peaucelle, Dimitri ; Lasserre, Jean-Bernard
Author_Institution :
LAAS-CNRS, Toulouse, France
Abstract :
For a linear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via quadratic-in-the-state Lyapunov functions polynomially dependent on the parameters. The contribution is twofold. First, if n denotes the system order and m the number of parameters, it is shown that it is enough to seek a parameter-dependent Lyapunov function of given degree 2nm in the parameters. Second, it is shown that robust stability can be assessed by globally minimizing a multivariate scalar polynomial related with this Lyapunov matrix. A hierarchy of LMI relaxations is proposed to solve this problem numerically, yielding simultaneously upper and lower bounds on the global minimum with guarantee of asymptotic convergence.
Keywords :
Lyapunov matrix equations; linear matrix inequalities; linear systems; stability; uncertain systems; LMI relaxation; Lyapunov matrix; asymptotic convergence; linear systems; multivariate scalar polynomial; parameter-dependent Lyapunov function; quadratic-in-the-state Lyapunov function; real parametric uncertainty; robust stability analysis; Convergence of numerical methods; Design methodology; Linear algebra; Linear matrix inequalities; Linear systems; Lyapunov method; Polynomials; Robust stability; Robustness; Uncertainty;
Conference_Titel :
Decision and Control, 2004. CDC. 43rd IEEE Conference on
Conference_Location :
Nassau
Print_ISBN :
0-7803-8682-5
DOI :
10.1109/CDC.2004.1428797