Linear quadratic regulator for a class of Markovian jump systems with control in jumps

This paper presents a suboptimal control strategy for the linear quadratic regulator problem of Markov jump linear systems subject to control in jumps. The system under study has a dual switching structure, in a manner that the system parameters jump according to both a Markov chain and a given switching control rule. The suboptimal control policy, derived via dynamic programming argument, relies on a special set of positive semidefinite matrices, in the sense that the number of elements of this set increases via a combinatorial step-by-step argument, applied at each time stage. An example is presented to illustrate the result.