Observability of Nonlinear Continuous­–Discrete Systems and Their Stabilization Using Asymptotic Observers

Abstract. This paper considers nonlinear dynamic systems described by a set of differential and difference equations and a nonlinear output equation. The states of such systems contain both continuous- and discrete-time components, so they are called continuous–discrete, or hybrid, dynamic control systems. For this class of systems, the issues of observability, design of full- and minimum-order observers, and stabilization with observers are investigated. A transition is performed from an original nonlinear hybrid system to a nonlinear discrete dynamic system equivalent in a natural sense. An observability criterion, sufficient conditions for the existence of full- and minimum-order asymptotic observers for nonlinear hybrid control systems, and sufficient conditions for the stabilization of a nonlinear hybrid system with designed asymptotic observers are established. Examples of designing asymptotic observers and stabilizing the augmented system with such observers are provided.

Keywords: continuous–discrete system, hybrid system, fully observable system, observer, stabilizing control.