Synthesis of robust discrete systems based on comparison with stochastic model

The problem of synthesis of the stabilizing control for a discrete linear system with uncertain parameters is considered. The stochastic model of comparison with parametric noise is constructed; the mean-square stability of this model implies the stability of the system with uncertain parameters varying in a given domain. For the case of the state feedback, the methods of synthesis of the robust stabilizing control based on the solution of either linear matrix inequalities or an auxiliary optimization problem with constraints in the form of linear matrix inequalities are proposed. The converging iterative algorithm of synthesis of the robust stabilizing control for the case of the output feedback is proposed. An example is given.