Predictor-Feedback Stabilization of Linear Switched Systems with State-Dependent Switching and Input Delay

TL;DR

This paper introduces a predictor-feedback control method for linear systems with state-dependent switching and input delays, ensuring stability through novel Lyapunov functionals and backstepping transformations.

Contribution

It presents a new exact predictor state construction for state-dependent switching systems with input delay, extending nonlinear delay control techniques.

Findings

Achieves uniform exponential stability of the closed-loop system.

Validates the control design through simulation with network-inspired switching.

Introduces a backstepping transformation for stability analysis.

Abstract

We develop a predictor-feedback control design for a class of linear systems with state-dependent switching. The main ingredient of our design is a novel construction of an exact predictor state. Such a construction is possible as for a given, state-dependent switching rule, an implementable formula for the predictor state can be derived in a way analogous to the case of nonlinear systems with input delay. We establish uniform exponential stability of the corresponding closed-loop system via a novel construction of multiple Lyapunov functionals, relying on a backstepping transformation that we introduce. We validate our design in simulation considering a switching rule motivated by communication networks.