Semistability, Finite-Time Stability, Differential Inclusions, and Discontinuous Dynamical Systems Having a Continuum of Equilibria

Author

Hui, Qing ; Haddad, Wassim M. ; Bhat, Sanjay P.

Author_Institution

Dept. of Mech. Eng., Texas Tech Univ., Lubbock, TX, USA

Volume

54

Issue

10

fYear

2009

Firstpage

2465

Lastpage

2470

Abstract

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for semistability and finite-time semistability for autonomous differential inclusions are established.

Keywords

Lyapunov methods; nonlinear dynamical systems; sampled data systems; stability; Lyapunov stable equilibrium point; convergence; differential inclusion; discontinuous autonomous dynamical system; discontinuous vector field; equilibria continuum; finite-time stability; nonlinear dynamic system; semistability; system initial condition; Aerodynamics; Asymptotic stability; Communication system control; Control systems; Lyapunov method; Mechanical systems; Network topology; Stability analysis; Sufficient conditions; Testing; Differential inclusions; Filippov solutions; discontinuous systems; finite-time stability; semistability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2029397

Filename

5256204