Further Results on Stabilization of Linear Systems with Time-varying Input Delay*

Abstract

This paper deals with stabilization of continuous-time linear systems affected by uncertain time-varying input delay. Existing solutions usually augment the state vector with the previous input and make use of standard robust stability analysis and synthesis techniques. Instead of discarding knowledge of the previous input, we employ a relaxed version of control Lyapunov functions (CLFs) that can cope with the additive term formed by the previous input. By solving an optimization problem on-line, in a receding horizon manner, we allow the CLF to be locally non-monotone, while taking into account state and input constraints. We then propose a special constraint that governs the non-monotonicity of the CLF such that attractivity is still attained. Moreover, we show that for CLFs defined using the infinity norm the developed method can be implemented as a single linear program, which can be solved explicitly via multiparametric programming. The developed theory is validated on a benchmark example: control of a DC-motor affected by time-varying input delay.