Geometric analysis of nonlinear impulsive control systems: Decompositions, accessibility, observability

Abstract

This paper investigates some fundamental properties of nonlinear impulsive control systems (ICS), including structural decompositions, accessibility and observability. By defining suitable invariant distributions using differential geometry methods, we propose the controllability decomposition and the observability decomposition for nonlinear ICS. With the help of such structural decompositions, the geometrical characterizations of the reachable set and the indistinguishable set of nonlinear ICS are presented. The corresponding criteria for (strong) accessibility and observability of nonlinear ICS are obtained. For a special class of linear ICS, we show that the strong accessibility is equivalent to the controllability. Finally, examples illustrate the effectiveness of the main theoretical results.