H 2 optimal control for a wide class of discrete-time linear stochastic systems

Abstract

In this article, the problem of H 2-control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Different H 2 performance criteria (often called H 2-norms) are introduced and characterised via solutions of some suitable linear equations on certain spaces of symmetric matrices. Some aspects specific to the discrete-time framework are revealed. The problem of optimisation of H 2-norms is solved under the assumption that full state vector is available for measurements. One shows that among all stabilising controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilising solution of a system of discrete-time generalised Riccati equations.