Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.