Observations-weighted controllers for linear stochastic systems using a dual criterion: the multivariable case

Abstract

The solution of a dual criterion observations-weighted control problem is obtained, using the polynomial equation approach, for linear, stochastic, multivariable, discrete-time systems. The system model involves input disturbance, and reference and coloured measurement noise signals. The dual criterion considered here includes the sensitivity functions in addition to the usual observations-weighted cost function. It is shown that the observations-weighted controller presented guarantees the internal stability of the closed-loop system, even in a light control for non-minimum-phase plants, whenever the sensitivity and/or complementary sensitivity weighting matrices are non-zero. The controller is also effective for improving the robustness of the usual observations-weighted controller, but has comparable computation loads to the dual criterion linear quadratic gaussian (LQG) controller in a general situation.