Linearization of expectation-based inequality conditions in control for discrete-time linear systems represented with random polytopes

Abstract

A technique of linearizing what we call expectation-based inequality conditions is proposed for control of discrete-time linear systems with stochastic dynamics. In particular, the coefficient random matrices of the systems are assumed to be represented with random polytopes, and the linearization technique is discussed so as to appropriately deal with associated uncertainties. Our expectation-based inequality is an inequality that involves decision variables contained in the expectation operation, and has a unique difficulty in direct linearization, in general. Hence, two key lemmas are provided so that the decision variables can be taken out from the expectation operation. The combinational use of such lemmas and the conventional linear matrix inequality (LMI) techniques, which is nothing but our linearization technique, is expected to be useful for transforming various kinds of expectation-based nonlinear inequality into numerically solvable standard LMIs. As a demonstration, new robust stability conditions are derived with the technique, whose effectiveness is confirmed numerically.