Application of the difference lmis method to robust stochastic H∞ control and filtering of distinct plants

A recently developed method is applied to the solution of linear matrix inequalities over a finite horizon for stochastic, state-multiplicative, linear, discrete-time varying systems with or without uncertainties. The method is used to solve a variety of problems beginning with the stochastic H_∞ discrete-time bounded real lemma and extending to robust state-feedback control, robust a priori and a posteriori filtering, robust H_∞ general-filtering and static output-feedback control design of uncertain systems. In all the above cases a solution is presented in the form of difference linear matrix inequalities. An example is brought which demonstrates the efficiency of the method.