Jump linear quadratic Gaussian problem for a class of nonhomogeneous Markov jump linear systems

This paper concerns with the jump linear quadratic Gaussian problem for a class of nonhomogeneous Markov jump linear systems (MJLSs) in the presence of process and observation noise. By assuming that mode transition rate matrices (MTRMs) are piecewise homogeneous whose variation is subjected to a high‐level Markov process, two Markov processes are proposed to model the characteristics of nonhomogeneous MJLSs: the variation of system mode is governed by a low‐level Markov process, while the variation of MTRM is governed by a high‐level one. Based on this model, a mode‐MTRM‐based optimal filter is firstly given where filter gain can be obtained via coupled Riccati equations. Secondly, we extend the separation principle of the linear quadratic problem to the nonhomogeneous MJLSs case. An optimal controller is then designed to minimize the quadratic system cost. Finally, a potential application in solar boiler system is given to illustrate the developed theoretical methods.