Finite-time H∞ control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities

2013 ◽  
Vol 350 (7) ◽  
pp. 1944-1961 ◽  
Author(s):  
Andong Liu ◽  
Li Yu ◽  
Dan Zhang ◽  
Wen-an Zhang
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Transition Probabilities ◽  
Genetic Regulatory Networks ◽  
Random Delays ◽  
Partly Unknown Transition Probabilities

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

2016 ◽  
Vol 71 (4) ◽  
pp. 289-304 ◽  
Author(s):  
R. Sakthivel ◽  
M. Sathishkumar ◽  
B. Kaviarasan ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Interval ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity of the obtained results.

Finite-time H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities

2013 ◽  
Vol 91 (12) ◽  
pp. 1020-1028 ◽  
Author(s):  
Jun Cheng ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yuping Zhang ◽  
Guihua Li
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Partial Information ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Partly Unknown Transition Probabilities ◽  
Stability And Stabilization ◽  
Jump Systems

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.

H∞ filtering for discrete-time genetic regulatory networks with random delays

2012 ◽  
Vol 239 (1) ◽  
pp. 97-105 ◽  
Author(s):  
Andong Liu ◽  
Li Yu ◽  
Wen-an Zhang ◽  
Bo Chen
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Random Delays

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

Complexity ◽  
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.

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.

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