Decision‐control mechanism for Markovian jump linear systems with Gaussian noise

This paper investigates the decision–control mechanism for Markovian jump linear systems with Gaussian noise. The mechanism here consists of two parts: decision to govern the mode transition rate matrix and output‐feedback controller to govern system state. Motivated by this, a joint index is put forward to evaluate system performance, which is a combination of traditional jump linear quadratic Gaussian cost and additional decision cost because extra expenses will be taken for adopting decision to mode transition rate matrix. For the minimization of joint index, the designing of optimal decision–control pair is deduced to the seeking of optimal decision. Meanwhile, the optimal decision can be obtained via an iterative with its convergence proved. Numerical examples illustrate the validity of the proposed mechanism.