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Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

We have accepted thirty-six papers in this special issue. In the published papers, eight consider the stability and stabilization problems of stochastic systems. There are fourteen papers which discuss the problems of the controller design and relevant optimization algorithms. Six articles study the system modeling and identification methods. One paper focuses on the fault detection for wireless networked control systems with stochastic uncertainties and multiple time delays, and seven consider the state estimation and filtering problems.

The problems of stochastic stability and stabilization problems of Markovian jumping systems have been extensively studied by many researchers, and many relevant results have been made. The paper entitled “_{∞}_{∞} performance analysis for a class of uncertain Markovian jumping systems with multiple delays. The paper entitled “

In recent years, the research on control optimization for stochastic dynamic systems has received more and more attention. For the_{∞} control aspects, the paper entitled “_{∞}_{∞}_{∞}_{∞} control performance analysis of continuous-time systems with random abrupt changes. The paper entitled “_{∞}_{∞} control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. The paper entitled “_{∞}_{∞} control problem for stochastic systems with Markovian jumping parameters and random packet losses. The paper entitled “_{∞} control problems for Markovian jump systems with time-varying delays, actuator saturation, and polytopic uncertain transition description; the paper entitled “_{∞}_{∞} control problem of uncertain neutral time-delayed system. For the predictive control aspects, the paper entitled “

Over the past few decades, the signal processing, estimation, and filtering problems have long been the mainstream of research topics. For the filtering problems, the paper entitled “_{∞}_{∞} filter for a class of nonlinear systems described by the Takagi-Sugeno fuzzy model, and the paper entitled “_{∞}_{∞} filtering problem for a kind of Takagi-Sugeno’s fuzzy stochastic system with time-varying delay and parameter uncertainties. For the state estimation problems, the paper entitled “

As is well known that the system modeling and identification are very useful in engineering applications, the paper entitled “

Although the selected topics and published papers are not a comprehensive representation of stochastic Markovian jumping systems, the authors represent the rich and many-faceted knowledge and we still hope the reader will find our special issue very useful.

We first express our great appreciation to all the authors of this special issue for their high quality contributions. All the reviewers’ efforts in reviewing the papers are also very greatly acknowledged.