Robust Reduced-order $H_{infty} $ Output-Feedback Control of Retarded Stochastic Linear Systems

摘要

A method for designing reduced-order output-feedback controllers for linear time-invariant retarded systems with state-multiplicative Wiener-type noise is introduced, which achieves a minimum bound on the $H_{infty } $ performance level. A cost function is defined that is the expected value of the standard $H_{infty} $ performance cost with respect to the stochastic parameters. A solution is thus obtained, for the reduced-order $H_{infty } $ output-feedback control problem, for the stationary case, via the input-output approach where the system is replaced by a non-retarded one, that contains deterministic norm-bounded uncertainties. The results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope. A numerical example, taken from the field of aircraft control, is given that demonstrates the applicability of the theory developed.