Analysis and Synthesis of Stochastic Nonlinear Systems

Abstract

Ever since the emergence of stochastic stabilization theory in the 1960s, stochastic systems have been widely studied and introduced in the areas of mathematics and engineering over the past few years. It should be noted that the stochastic dynamical system is a dynamical system subjected to the effects of noise, and the effects of fluctuations have been receiving increasing interest. The stochastic abrupt changes, such as sudden environment changes and repairs of components and random failures, always exist in the variable structures during the stochastic dynamical systems; the nonlinearity occurs in the real engineering applications. Nowadays, researches on stochastic nonlinear systems have received significant attention due to their wide applications in various fields such as physics, technology, and life sciences. Therefore, the analysis and synthesis of stochastic nonlinear systems play important roles in many practical systems.In the light of above considerations, this special issue has been launched. Up to now, papers were submitted by researchers in various research fields from different countries, and a total number of papers are included in this special issue. The accepted reviewed papers can be categorized into five groups: nonlinear Markovian jump systems, neural networks with external constant input vector, noise included nonlinear oscillator, Brownian Motions, and other nonlinear character applications.In nonlinear Markovian jump systems, H. Dong and J. Chen introduced concerned with the ∞ filtering for a class of networked Markovian jump systems with multiple communication delays. The stochastic communication delays are considered in the filter design. L. Li et al. investigated ∞ fuzzy control for a class of nonlinear singular Markovian jump systems where time delay under consideration is described by Takagi-Sugeno (T-S) fuzzy models. B. Yan et al. considered the full information of underlying Markov process; ∞ filtering is designed for underlying closed-loop singular Markovian jump system while system state does not exceed a given bound over some finite time interval.In neural networks with external constant input vector, with a suitable Lyapunov-Krasovskii functional (LKF) and Writinger-based integral inequality, M. J. Park proposed the sufficient conditions for guaranteeing the asymptotic stability of the concerned networks which are derived in terms of linear matrix inequalities. J. Tian and Y. Liu established some less conservative stability criteria in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and using the reciprocally convex approach. W. Wen and K. Shi proposed some new less conservative conditions by taking fully the relationship between the terms in the Leibniz-Newton formula and some effective mathematical techniques and a convex optimization approach into account. L. Hou and H. Zhu investigated the stability of stochastic discrete-time neural networks (NNs) with discrete time-varying delays and leakage delay...