In this paper robust stability of state space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the Homogeneous Polynomially Parameter-Dependent Quadratic Lyapunov Functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists a HPD-QLF. The main result of the paper is a sufficient condition for determining the sought HPD-QLF, which amounts to solving Linear Matrix Inequalities (LMIs) derived via the Complete Square Matricial Representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions / G. Chesi; A. Garulli; A. Tesi; A. Vicino. - STAMPA. - 5:(2003), pp. 4670-4675. (Intervento presentato al convegno 42nd IEEE Conference on Decision and Control tenutosi a Maui, HI, USA nel 9 December 2003 through 12 December 2003) [10.1109/CDC.2003.1272307].
Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions
TESI, ALBERTO;
2003
Abstract
In this paper robust stability of state space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the Homogeneous Polynomially Parameter-Dependent Quadratic Lyapunov Functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists a HPD-QLF. The main result of the paper is a sufficient condition for determining the sought HPD-QLF, which amounts to solving Linear Matrix Inequalities (LMIs) derived via the Complete Square Matricial Representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
