State and mode feedback control for discrete-time Markovian jump linear systems with controllable MTPM

Abstract

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems &#x0028 MJLSs &#x0029 with controllable mode transition probability matrix &#x0028 MTPM &#x0029 are investigated. In most achievements, controller design of MJLSs pays more attention to state &#x002F output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state &#x002F output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.