On the stability of predictive controllers for linear systems with variable time delays

In this article, a method for computing a control law for discrete linear systems with variable time delays using predictive tools and stability conditions is presented. The system is written as a switched system. A state feedback is then computed for each mode using predictive control. It is shown that a nonlinear optimization problem can be formulated in order to obtain a control law which gives the best approximation of the state feedback control previously computed for each mode. This formulation ensures stability since stabilization conditions are also included through a common Lyapunov function. The optimization problem is then transformed to a problem with Bilinear Matrix Inequalities (BMI) constraints whose solution can be easily computed. Several examples show the feasibility and the efficiency of the approach.