Lyapunov matrices for the stability analysis of a system with state and input delays and dynamic predictor control

Abstract

In this work, we describe a method to compute the Lyapunov matrix of a system with state and input delay when the input is a dynamic predictor-based control law. We observe that this system can be represented in an extended state-space form. The resulting model is a system with multiple distributed time-delays with repeated piecewise kernels. We present a scalar case study involving the Lyapunov matrix construction. The obtained Lyapunov matrix allows us to carry out the stability analysis in the time domain. Finally, some remarks about the dynamic and the simple predictor-based control laws are given.