Robust D-stability via discrete controllers for continuous-time uncertain systems with multiple delays

Abstract

This work addresses the allocation of closed-loop poles of a discretized system from a continuous-time one with multiple input delays, aiming at its control through a computer. In order to handle a practical challenge presented in Network Control System (NCS) approaches, uncertain sampling period, distinct input time delays and parametric uncertainties in polytopic form can be propagated from the original state space representation to the discretized state model. The resulting discrete-time time-delay system has a very specific feature, so that it can be converted into an augmented linear system without time-delay. In this context, the main contribution of the present paper consists of a Linear Matrix Inequality (LMI) based control synthesis condition composed of homogeneous polynomial matrices of arbitrary degree, which ensures the continuous-time system stability and simultaneously the allocation of the closed-loop poles of the augmented system in a D-stable region. Numerical simulations illustrate the exposed.