Input Delay Compensation for a Class of Switched Linear Systems via Averaging Exact Predictor Feedbacks

Abstract

The key challenges in design of predictor-based control laws for switched systems with arbitrary switching and long input delay are the potential unavailability of the future values of the switching signal (at current time) and the fact that dwell time may be arbitrary. In the present paper, we resolve these challenges developing a new predictor-based control law that is, essentially, an average of exact predictor feedbacks, each one corresponding to an exact predictor-feedback law for a system that operates only in a single mode. Because the predictor state in our control design does not correspond to an exact predictor, stability can be guaranteed under a restriction on the differences among the system's matrices and controller's gains. This is an unavoidable limitation, for a switching signal whose future values may be unavailable, when no constraint is imposed on the values of delay and dwell time (as it is the case here). We establish (uniform) stability of the closed-loop system employing a Lyapunov functional. The key step in the stability proof is constructive derivation of an estimate of the mismatch between an exact predictor feedback and the average of predictor feedbacks constructed. We illustrate the performance of the proposed predictor-based control law in simulation, including comparisons with alternative, predictor-based control laws.