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 l(2)-gain of the closed-loop where a cost function is defined to be the expected value of the standard H-infinity performance index with respect to the stochastic uncertainty. An example is given that demonstrates the merit of the theory. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.