State-multiplicative Noisy Systems: Robust H_∞ Output-Feedback Control

Linear discrete-time systems with stochastic and deterministic polytopic type uncertainties in their state-space model are considered. A dynamic output-feedback controller is obtained via a new approach which allows a derivation of a controller in spite of parameter uncertainty. In the proposed approach the system is described via a difference equation and an augmented system is then used to obtain the output-feedback controller parameters. The controller is obtained without assuming a specific structure to the quadratic Lyapunov function and it is the first time that an output-feedback controller is obtained for robust state-multiplicative systems. The controller minimizes the stochastic l₂-gain of the closed-loop where a cost function is defined to be the expected value of the standard H_∞ performance index with respect to the stochastic uncertainty. An example is given that demonstrates the merit of the theory.