Finite-time boundedness filtering for discrete-time Markovian jump system subject to partly unknown transition probabilities

This paper addresses the problems of finite-time stochastic stability and stabilization for linear Markovian jump systems subject to partial information on the transition probabilities. By introducing bounded finite time and stochastic character, sufficient conditions that can ensure bounded finite time and H∞ finite-time bounded filtering are derived. Finally, an example is given to illustrate the efficiency of the proposed method.

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Finite-time stochastic stability and stabilisation of linear discrete-time Markovian jump systems with partly unknown transition probabilities

IET Control Theory and Applications ◽

10.1049/iet-cta.2011.0335 ◽

2012 ◽

Vol 6 (10) ◽

pp. 1522-1526 ◽

Cited By ~ 50

Author(s):

Z. Zuo ◽

H. Li ◽

Y. Wang ◽

Y. Liu

Keyword(s):

Discrete Time ◽

Stochastic Stability ◽

Finite Time ◽

Transition Probabilities ◽

Markovian Jump Systems ◽

Markovian Jump ◽

Partly Unknown Transition Probabilities ◽

Jump Systems

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Finite-Time H∞ Filtering for Discrete-Time Singular Markovian Jump Systems with Time Delay and Input Saturation

Complexity ◽

10.1155/2019/4675397 ◽

2019 ◽

Vol 2019 ◽

pp. 1-22

Author(s):

Wei Guan ◽

Lei Fu ◽

Yuechao Ma

Keyword(s):

Discrete Time ◽

Finite Time ◽

Transition Probabilities ◽

Input Saturation ◽

Markovian Jump Systems ◽

Time Interval ◽

Markovian Jump ◽

Partly Unknown Transition Probabilities ◽

Singular Markovian Jump Systems ◽

Jump Systems

The paper is discussed with the problem of finite-time H∞ filtering for discrete-time singular Markovian jump systems (SMJSs). The systems under consideration consist of time-varying delay, actuator saturation and partly unknown transition probabilities. We pay attention to the design of a H∞ filtering which ensures the filtering error systems to be singular stochastic finite-time boundedness. By employing an adequate stochastic Lyapunov functional together with a class of linear matrix inequalities (LMIs), a sufficient condition is firstly established, which guarantees the systems to achieve our goal and satisfy a prescribed H∞ attenuation level in the given finite-time interval. Considering the above conditions, a distinct presentation for the requested H∞ filter is given. Finally, two numerical examples add to a dynamical Leontief model of economic systems are presented to illustrate the validity of the developed theoretical results.

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

Abstract and Applied Analysis ◽

10.1155/2014/597298 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Li Liang

Keyword(s):

Neural Networks ◽

Finite Time ◽

Transition Probabilities ◽

The State ◽

Time Interval ◽

Finite Time Interval ◽

Markovian Jumping ◽

Stochastic Boundedness ◽

Partly Unknown Transition Probabilities ◽

Finite Time Boundedness

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.

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