Robust finite-time estimation of Markovian jumping systems with bounded transition probabilities

2013 ◽  
Vol 222 ◽  
pp. 297-306 ◽  
Author(s):  
Shuping He ◽  
Fei Liu
Keyword(s):  
Finite Time ◽  
Transition Probabilities ◽  
Time Estimation ◽  
Markovian Jumping ◽  
Markovian Jumping Systems

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

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.

scholarly journals Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Ma
Keyword(s):  
Finite Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
The Mean ◽  
Delay Dependent ◽  
Passivity And Passification ◽  
Theoretical Results

This paper investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.

scholarly journals Stochastic Finite-Time Guaranteed Cost Control of Markovian Jumping Singular Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Yingqi Zhang ◽  
Caixia Liu ◽  
Xiaowu Mu
Keyword(s):  
Finite Time ◽  
Cost Control ◽  
Transition Probabilities ◽  
Singular Systems ◽  
Singular System ◽  
Sufficient Conditions ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Markovian Jumping ◽  
Guaranteed Cost

The problem of stochastic finite-time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the definitions of stochastic singular finite-time stability, stochastic singular finite-time boundedness, and stochastic singular finite-time guaranteed cost control are presented. Then, sufficient conditions on stochastic singular finite-time guaranteed cost control are obtained for the family of stochastic singular systems. Designed algorithms for the state feedback controller are provided to guarantee that the underlying stochastic singular system is stochastic singular finite-time guaranteed cost control in terms of restricted linear matrix equalities with a fixed parameter. Finally, numerical examples are given to show the validity of the proposed scheme.

scholarly journals Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

scholarly journals Resilient - Filtering of Uncertain Markovian Jumping Systems within the Finite-Time Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shuping He
Keyword(s):  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
Finite Time Boundedness

This paper studies the resilient - filtering problem for a class of uncertain Markovian jumping systems within the finite-time interval. The objective is to design such a resilient filter that the finite-time - gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. Based on the selected Lyapunov-Krasovskii functional, sufficient conditions are obtained for the existence of the desired resilient - filter which also guarantees the stochastic finite-time boundedness of the filtering error dynamic systems. In terms of linear matrix inequalities (LMIs) techniques, the sufficient condition on the existence of finite-time resilient - filter is presented and proved. The filter matrices can be solved directly by using the existing LMIs optimization techniques. A numerical example is given at last to illustrate the effectiveness of the proposed approach.

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