Convergence within a polyhedron: controller design for time-delay systems with bounded disturbances

This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closed-loop system converges within a pre-specified polyhedron. Based on the Lyapunov-Krasovskii method combining with the free-weighting matrix technique, a new sufficient condition for the existence of a static output feedback controller is derived. The author's condition is expressed in terms of linear matrix inequalities with two parameters need to be tuned and therefore can be efficiently solved by using a two-dimensional search method combining with convex optimisation algorithms. To be able to obtain directly an output feedback control matrix from the derived condition, they propose an appropriate combination between a state transformation with a choice of a special form of the free-weighting matrices. The feasibility and effectiveness of the derived results are illustrated through five numerical examples.