Asynchronous Control for Positive Markov Jump Systems
- PDF / 521,807 Bytes
- 9 Pages / 594.77 x 793.026 pts Page_size
- 78 Downloads / 238 Views
ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Asynchronous Control for Positive Markov Jump Systems Kai Yin, Dedong Yang*, Jiao Liu, and Hongchao Li Abstract: A new result is provided for the asynchronous control analysis of positive Markov jump systems (PMJSs) in this paper. Firstly, a hidden Markov model is described to express the asynchronous circumstances that appear between the system modes and controller modes. Secondly, by utilizing a copositive stochastic Lyapunov function, a sufficient and necessary condition is given to guarantee the mean stability of PMJSs. Thirdly, we obtain another equivalent condition and design the corresponding asynchronous controller. Finally, the correctness of these results is verified by two numerical examples. Keywords: A hidden Markov model, asynchronous control, copositive stochastic Lyapunov function, positive Markov jump systems.
1.
INTRODUCTION
As a special class of stochastic hybrid systems, positive Markov jump systems (PMJSs) have recently aroused great concern of researchers and engineers because of its applications in some practical systems, such as Power allocation in telecommunication networks [1], pest structured population dynamic systems [2], SIS Epidemiological Models [3] and so on. So far, some substantial results on PMJSs have been reported in [4ā15]. In [4], by using linear matrix inequality (LMI) technology, sufficient and necessary conditions have been derived for continuoustime PMJSs. The mean stability and stabilization issues have been discussed for PMJSs in [5], where the obtained conditions have existed in the form of linear programming. Compared with LMI technology in [4], the linear programming strategy in [5] is more effective due to the lower computational complexity. The authors in [6] have considered the mean stability issue for PMJSs with homogeneous and switching transition probabilities. The problem of finite-time sliding mode control has been also analyzed by [7] for nonlinear PMJSs. The positive filter design issue has been examined for the discrete-time and the continuous-time PMJSs in [8] and [9], respectively. In [10] and [11], it has been discussed for the positive observer design issue of PMJSs. And the work in [12ā15] has also studied the effects of time-delays for PMJSs. The positivity constraint of positive systems will have some effects for the stability analysis, which is also a motivation of intensive research at present.
However, most existing results are based on a common assumption that the controller/filter modes can match the original system modes in real time, that is, synchronization. The development of synchronization controller has been explored in literature [16ā20]. In fact, there exists a phenomenon that the controller/filter modes can not run in full synchronization with the system modes, which is called as asynchronous phenomenon and leads to the result that the asynchronous control issues arise. The problem of asynchronous l2 -lā filtering for discrete-time Markov jump systems (MJSs) has been ad
Data Loading...
