Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2029397