Computation of bounds for permanence time in polytopes for nonlinear systems

Abstract

Diverse control strategies require determining how long the state of a system remains within a considered region. This often arises in switching control strategies, where the goal is to select the current mode to ensure that the state stays inside the region for as long as possible. In general, nonlinear system equations do not admit analytical closed-form solutions; thus, only approximate solutions are available, usually obtained through numerical integration methods. This work presents a method to guarantee that, based on approximate solutions, the exact solution remains within a desired convex set over a time interval. We show that when the set in question is polytopic, the required computations become simpler. The method is applied to a nonlinear system to illustrate its operation.