Design of guaranteed cost overlapping controllers for a class of uncertain state-delay systems

The paper deals with a class of linear continuous-time state-delay systems with norm-bounded uncertainties which are composed by overlapped subsystems. The main goal is to design overlapping guaranteed cost controllers for this class of systems by using the corresponding feasible solution of a linear matrix inequality (LMI) problem. In the overlapping decompositions context the selection of so-called complementary matrices is crucial. The paper presents a procedure to obtain numerical complementary matrices such that a bounded cost of the quadratic performance index is minimized. A simple example is supplied to illustrate the use of the proposed strategy.