Abstract
This paper considers the stabilization of continuous-time Markovian jump systems (MJSs) via a restricted controller. It is actually a period and random switching controller. It also contains some existing controllers as special ones. Sufficient conditions for existence of such a controller are established by studying a discrete-time MJS, which are presented in terms of LMIs and depend on its period and probability. Moreover, an extension about a similar but aperiodic controller is considered. Finally, a numerical example is used to demonstrate the effectiveness and superiority of the proposed methods.
Highlights
It is known that Markovian jump system (MJS) [1], [2] is a particular kind of hybrid systems
A lot of topics on all kinds of MJSs have been studied such as stability [3]–[6], stabilization [7]–[13], H∞ control [14]–[16] and filtering [17]–[21], fault detection [22]–[24], estimation [25], [26], adaptive control [27], [28], synchronization [29], and so on
One of them is that the jump points are periodic, and the dwell times are equal or constant
Summary
It is known that Markovian jump system (MJS) [1], [2] is a particular kind of hybrid systems. It is said that such a fast switching will lead to a higher cost even a damage to an equipment In this case, it is natural to design a controller for an MJS which could sustain a period. Because of its sojourn time being any distribution, the corresponding switching will be slower than one of traditional MJSs. Very recently, the stability and stabilization of discrete-time semi-Markov jump linear systems subject to exponentially modulated periodic probability density function of sojourn time was considered in [35] and very important to make further research about semiMarkov jump systems. The main contributions of this paper are summarized as follows: 1) A kind of restricted controller in terms of period and random switching is proposed, which contains some existing controllers as special ones; 2) By studying a discrete-time MJS indirectly, sufficient linear matrix inequality conditions for the controller are presented, in which both period and conditional switching probabilities are included. We use ‘‘∗ as an ellipsis for the terms induced by symmetry, diag {· · ·} for a block-diagonal matrix, and (M ) M + M T
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