Abstract
This paper considers the problem of asynchronous observer-based finite-horizon control of Markov jump systems (MJSs) with actuator saturations. The hidden Markov model is employed to describe asynchronous phenomenon between observer-based controller and the plant, where the observer designed has its own jumping mode that is different from that of the controlled plant. The purpose of this paper is to develop an asynchronous observer-based controller to ensure that an H ∞ performance index, over a given finite-horizon, can be satisfied for MJSs with actuator saturation. A sufficient condition is derived to guarantee that the H ∞ performance index can be achieved by using the stochastic Lyapunov function theory and S-Procedure lemma. Then, a recursive linear matrix inequality (RLMI) approach is applied to design the gains of the controller and observer. Finally, an example is given to verify the proposed algorithm.
Highlights
In the past decades, Markov jump systems (MJSs), as a special type of the hybrid system, can be widely used to describe the dynamics of some practical systems subject to random variations coming from the unpredictable external disturbances, failures or repairs of components
Many results associated with different performance indexes including stabilization problem, passivity, dissipativity, state estimation/ filtering and H∞ performance, etc., for MJSs have been investigated by employing different approaches
The sufficient condition of achieving a prescribed H∞ performance is derived by employing Lyapunov based method, S-Procedure Lemma and the recursive linear matrix inequality (RLMI) approach
Summary
Markov jump systems (MJSs), as a special type of the hybrid system, can be widely used to describe the dynamics of some practical systems subject to random variations coming from the unpredictable external disturbances, failures or repairs of components. Many results associated with different performance indexes including stabilization problem, passivity, dissipativity, state estimation/ filtering and H∞ performance, etc., for MJSs have been investigated by employing different approaches. [1] studied the stabilization problem of MJSs subject to time-varying delays and the partially known transition probabilities. The state estimation problem of MJSs has been discussed by employing the sliding-mode control approaches in [2] and the same method has been developed to consider the dissipativity problem in [3]. Other performances related approaches for MJSs can be found in [4]–[6], just to name a few.
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