Computation of controlled invariant sets for discrete-time switched nonlinear systems with time-delay

Abstract

We consider the concept of set invariance for discrete-time switched nonlinear systems with time-delays, referred to here as D-invariance. Specifically, the existence of controlled invariant sets for nonlinear switched systems with time-delay is proved by defining a suitable predecessor operator. As the main contribution, we use the interval analysis method to iteratively computing the inner-approximation of a controlled D-invariant set, which is a key step towards invariance control of switched nonlinear systems with time-delay. The sequence of the approximated controlled D-invariant sets are obtained by considering all possible delays within a given bounded region of the state space, so that a D-invariant set and controller that are independent of time-delay are obtained. Finally, two examples are given to show the performance of this method.