Title :
Stability theory for hybrid dynamical systems
Author :
Ye, Hui ; Michel, Anthony N. ; Hou, Ling
Author_Institution :
Dept. of Electr. Eng., Notre Dame Univ., IN, USA
Abstract :
Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system are of great current interest. In the present paper we first formulate a definition of hybrid dynamical system which covers a very large number of classes of hybrid systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the notion of invariant set (e.g., equilibrium) for hybrid dynamical systems and we define several types of (Lyapunov-like) stability concepts for an invariant set. We then establish sufficient conditions for the uniform stability and the uniform asymptotic stability of an invariant set of a hybrid dynamical system. Under some mild additional assumptions, we also establish necessary conditions for some of the above stability types (converse theorems). To demonstrate the applicability of the developed theory, we present two specific examples of hybrid dynamical systems and we conduct a stability analysis of one of these examples (a sampled-data feedback control system with a nonlinear (continuous-time) plant and a linear (discrete-time) controller)
Keywords :
Lyapunov methods; stability; stability criteria; Lyapunov-like stability concepts; converse theorems; dynamic behavior; equilibrium; hybrid dynamical systems; invariant set; qualitative analysis; sampled-data feedback control system; stability analysis; stability theory; uniform asymptotic stability conditions; Asymptotic stability; Control systems; Ducts; Eigenvalues and eigenfunctions; Extraterrestrial measurements; Feedback control; Linear feedback control systems; Logic; Stability analysis; Sufficient conditions;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.478517