Study on neutral complex systems with Markovian switching and partly unknown transition rates
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ORIGINAL ARTICLE
Study on neutral complex systems with Markovian switching and partly unknown transition rates Xinghua Liu1,2 • Guoqi Ma1 • Hongsheng Xi1
Received: 11 October 2015 / Accepted: 20 September 2016 Ó Springer-Verlag Berlin Heidelberg 2016
Abstract The exponential stability problem of uncertain neutral complex system with Markovian switching is investigated in the presence of nonlinear perturbations and partial information on transition rates. The study begins to consider the related nominal systems and construct a novel augmented stochastic Lyapunov functional which contains some triple-integral terms to reduce the conservatism. Then the exponential stability criteria are developed by utilizing Lyapunov stability theory, reciprocally convex lemma and free-weighting matrices. The results are further extended to the corresponding uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods. Keywords Markovian switching Neutral complex systems Interval mode-dependent time-varying delay Nonlinear perturbations
This work was supported in part by the National Key Scientific Research Project (61233003) and China Postdoctoral Science Foundation (2015M580549). & Xinghua Liu [email protected] Guoqi Ma [email protected] Hongsheng Xi [email protected] 1
Department of Automation, University of Science and Technology of China, Hefei, China
2
School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore
1 Introduction As a special switched system, Markovian jump systems (MJSs) have been widely considered in the past decades. As a matter of fact, many practical dynamics such as solar thermal central receivers, robotic manipulator systems, aircraft control systems, economic systems, etc., can be described as Markovian jump systems (MJSs) where the abrupt variation in their structures and parameters can be naturally represented by the jumps in MJSs. Since its first appearance in 1961, MJSs have received much attention, see, e.g., [1–8] and the references therein for more details. In view of these results, the transition probabilities in the jumping process determine the system behavior to a large extent. However, the likelihood of obtaining such available knowledge is actually questionable, and the cost is probably expensive. Thus it is significant and necessary, from control perspectives, to further study more general jump systems with partially known transition rates. Recently, many results on the Markovian jump systems with partially known transition rates are obtained [9–13]. Most of these improved results just require some free matrices or the knowledge of the known elements in transition rate matrix, such as the structures of uncertainties, and some else of the unknown elements need not be considered. It is a great progress on the analysis of Markovian jump systems. However, these results have conservativeness to some extent, which exist room for further improvement. On another research front line, time-dela
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