Robust stabilization subject to structured uncertainties and mean power constraint

This paper deals with a robust stabilization problem for discrete-time systems subject to multiple disturbances occurring in controller and actuating channel, where both linear structured uncertainties and white Gaussian noises are included. The desired control law is aimed to robustly stabilize the system and to satisfy some pre-specified mean power constraint, simultaneously. By the philosophy of the mixed H2∕H∞ control, a solvability condition is first derived for single-input systems that reveals the intrinsic relation between the unstable poles of the plant and the disturbance parameters, together with two cross-coupled algebraic Riccati equations. The result is further generalized to multiple-input systems with a sufficient condition given again by the unstable poles of the plant. An example is included to illustrate the current results.