Robust polytopic H∞ control of linear retarded state-multiplicative stochastic systems

Linear, state delayed, continuous-time systems are considered with both stochastic and polytopic type uncertainties in the state-space model. The problem of robust state-feedback and dynamic H
_∞
output-feedback control are solved, for the stationary case, via the input-output approach where the system is replaced by a nonretarded system having deterministic norm-bounded uncertainties. 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.