Estimation of stability regions of SDRE controlled systems using vector norms

Author

Erdem, E.B. ; Alleyne, Andrew G.

Author_Institution

Emmeskay Inc, Plymouth, MI, USA

Volume

1

fYear

2002

fDate

2002

Firstpage

80

Abstract

The origin of a state-dependent Riccati equation (SDRE) controlled system is an asymptotically stable equilibrium point. However, knowledge of its region of stability is also of practical importance. Obtaining a good estimate of the ROA for general nonlinear systems-especially of higher order-is a challenging task in itself. For SDRE controlled systems, the task becomes even more difficult since the closed-loop matrix is usually not available in closed form. Borne et al. (1996) and Richard et. al. (1988) proposed a new method for determining the stability of nonlinear systems. The method is based on defining an overvaluing comparison system for the original one by using vector norms. In this paper, an approach to estimate stability regions of SDRE controlled systems using this method is developed. Examples are given to illustrate the procedure.

Keywords

Riccati equations; asymptotic stability; matrix algebra; nonlinear control systems; performance index; time-varying systems; vectors; asymptotically stable equilibrium point; closed-loop matrix; general nonlinear systems; overvaluing comparison system; region of stability; stability regions; state-dependent Riccati equation controlled systems; vector norms; Control systems; Controllability; Feedback control; Linear systems; Nonlinear equations; Nonlinear systems; Optimal control; Performance analysis; Riccati equations; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2002. Proceedings of the 2002

ISSN

0743-1619

Print_ISBN

0-7803-7298-0

Type

conf

DOI

10.1109/ACC.2002.1024784

Filename

1024784