Abstract
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. It is the first time that an output-feedback controller is obtained for robust state-multiplicative systems. The controller minimizes the stochastic \(l_2\)-gain of the closed-loop system, where the cost function is defined to be the expected value of the standard \(H_{\infty }\) performance index with respect to the stochastic uncertainty. An example is given that demonstrates the merit of the theory.
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