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Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

DOI: 10.1155/2014/597298

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This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results. 1. Introduction Over the past decades, delayed neural networks have been successfully applied in the pattern recognition, signal processing, image processing, and pattern recognition problems. However, these successful applications mostly rely on the dynamic behaviors of delayed neural networks and some of these applications are dependent on stability of the equilibria of neural networks. Up to now, there have been a large number of results related to dynamical behaviors of delayed neural networks [1–8]. On the one, in the past few decades, Markovian jump systems have gained special research attention. Such class of systems is a special class of stochastic hybrid systems, which may switch from one to another at the different time. Such as component failures, sudden environmental disturbance and abrupt variations of a nonlinear system [9–11]. Moreover, it is shown that such jumping can be decided by a Markovian chain [12]. For the linear Markovian jumping systems, many important issues have been devoted extensively such as stability, stabilization, control synthesis, and filter design [13–16]. In reality, however, it is worth mentioning that most of the gotten results are based on the implicit assumptions that the complete knowledge of transition probabilities is known. It is known that in most situations, the transition probabilities rate of Markovian jump systems and networks is not known; it is difficult to obtain all the transition probabilities. Therefore, it is of great importance to investigate the partly unknown transition probabilities. Very recently, the systems with partially unknown transition probabilities have been fully investigated and many important results have been obtained; for a recent survey on this topic and related questions, one can refer to [17–23]. However, it has been shown that the existing delay-dependent results are conservative. On the other hand, the practical problems which described system stay as not

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