Bounded sample path control of discrete time jump linear systems

Abstract

A bounded sample path control strategy, based on the idea of minimizing an upper bound of the possible costs to go, is formulated. The finite and infinite versions of the JLQBSP (jump linear quadratic bounded sample path) problem are solved. A set of sufficient conditions for the existence and uniqueness of steady-state solutions that stabilize the controlled system with certainty (i.e. on any sample path) is also presented. The resulting costs are finite. The sufficient conditions are based on concepts of absolute controllability and observability of the jump linear system. This JLQBSP controller requires less precise information about form transition probabilities (only the directed interaction matrix is needed) and provides reliable control in all circumstances. Consequently, sometimes it is more appropriate for potential applications than JLQ control algorithms that are optimal in only an average sense