Robust Overlapping Guaranteed Cost Control of Uncertain State-Delay Discrete-Time Systems

This note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state-delayed discrete-time systems with norm bounded uncertainties using the concept of guaranteed cost control. Expansion-contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved, including conditions on the equality of guaranteed performance bounds. The controllers are designed in the expanded space using a linear matrix inequality (LMI) delay independent procedure specifically adapted to this class of problems. The designed controllers are then contracted and implemented into the original system. The results are specialized for the overlapping decentralized control design. The method enables an effective construction of block tridiagonal controllers. A numerical illustrative example is supplied