Robust H∞ filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation: The finite-horizon case

This article is posted with the permission of IEEE - Copyright @ 2011 IEEEThis paper addresses the robust H∞ filtering problem for a class of discrete time-varying Markovian jump systems with randomly occurring nonlinearities and sensor saturation. Two kinds of transition probability matrices for the Markovian process are considered, namely, the one with polytopic uncertainties and the one with partially unknown entries. The nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the Bernoulli distributions. The main purpose of this paper is to design a robust filter, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the time-varying Markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation. Sufficient conditions are established for the existence of the desired filter satisfying the H∞ performance constraint in terms of a set of recursive linear matrix inequalities. Simulation results demonstrate the effectiveness of the developed filter design scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303, and 61004067, National 973 Project under Grant 2009CB320600, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K., under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Output peak control of nonhomogeneous markov jump system with unit-energy disturbance

This paper considers output peak controller design for discrete nonhomogeneous Markov jump systems under unit-energy disturbance. The mode-dependent output peak feedback controller is designed to ensure that the resulting closed-loop system is stochastically stable and the peak of the output is within a specified range. Furthermore, the optimal energy-to-peak gain indices of the mode-dependent and the mode-independent state feedback controllers are evaluated and compared. A numerical example is presented to illustrate the applicability of the results obtained

Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates

This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. Based on linear matrix inequalities, the quantized state-feedback controller is formulated to ensure the closed-loop system is stable in mean square. Finally, a numerical example is presented to verify the validity of the developed theoretical results

Disturbance Attraction Domain Estimation for Saturated Markov Jump Systems with Truncated Gaussian Process

This paper investigates the disturbance attraction domain estimation of saturated Markov jump systems with truncated Gaussian process. The aim is to estimate the disturbance domain of attraction so that the state is maintained in a neighbour around the origin by a state feedback controller regardless of bounded disturbance. The problem is formulated as parameter-dependent linear matrix inequalities (LMIs). The optimal disturbance attraction domain is obtained through searching for most appropriate auxiliary parameters in the defined domain. A numerical example is presented to show the potential application of the results

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

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