Robust H_∞ output-feedback control of retarded state-multiplicative stochastic systems

Linear, state-delayed, continuous-time systems are considered with both stochastic and norm-bounded deterministic uncertainties in the state-space model. The problem of robust dynamic H_∞ output-feedback control is solved, for the stationary case, via the input-output approach where the system is replaced by a nonretarded system with additional deterministic norm-bounded uncertainties. A delay-dependent result is obtained which involves the solution of a simple linear matrix inequality. In this problem, a cost function is defined which is the expected value of the standard H _∞ performance cost with respect to the stochastic parameters. A practical example taken from the field of guidance control is given that demonstrates the applicability of the theory.