Passivity analysis and passification for a class of switched stochastic systems with time-varying delay

2013 ◽  
Vol 91 (12) ◽  
pp. 1049-1056 ◽  
Author(s):  
Huimei Jia ◽  
Zhengrong Xiang
Keyword(s):  
State Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Passivity Analysis ◽  
Switched Stochastic Systems ◽  
Delay Dependent ◽  
Varying Delay

This paper is concerned with the problems of passivity analysis and passification for a class of switched stochastic systems with time-varying delay. Firstly, based on the multiple storage functions approach, a delay-dependent sufficient condition for the underlying systems to be stochastically passive is derived in terms of linear matrix inequalities. Then, based on the obtained passivity condition, a state feedback passive controller is designed. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method.

New Delay-Dependent Robust Stability Criterion for Uncertain Stochastic Systems with Time-Varying Delays

2012 ◽  
Vol 461 ◽  
pp. 633-636
Author(s):  
Cheng Wang
Keyword(s):  
Robust Stability ◽  
Stability Criterion ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

The problem of delay-dependent robust stability of uncertain stochastic systems with time-varying delay is discussed in this paper. Based on the Lyapunov-Krasovskii theory and free-weighting matrix technique, new delay-dependent stability criterion is presented. The criterion is in terms of linear matrix inequality (LMI) which can be solved by various available algorithms.

scholarly journals Stability Analysis and RobustH∞Control of Switched Stochastic Systems with Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhengrong Xiang ◽  
Guoxin Chen
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Mean Square Exponential Stability ◽  
Varying Delay

The problems of mean-square exponential stability and robustH∞control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then,H∞performance is studied and robustH∞controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

scholarly journals H∞Control for Nonlinear Systems with Time-Varying Delay Using Matrix-Based Quadratic Convex Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
C. Emharuethai ◽  
P. Niamsup
Keyword(s):  
Nonlinear System ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Time Varying Delay ◽  
Varying Delay

H∞control problem for nonlinear system with time-varying delay is considered by using a set of improved Lyapunov-Krasovskii functionals including some integral terms, and a matrix-based on quadratic convex, combined with Wirtinger's inequalities and some useful integral inequality.H∞controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theH∞state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

New Delay-Dependent Stability Criteria for Systems with Interval Time-Varying Delay

2011 ◽  
Vol 48-49 ◽  
pp. 734-739 ◽  
Author(s):  
Dong Sheng Xu ◽  
Jun Kang Tian
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Integral Term ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with delay-dependent stability for systems with interval time varying delay. By defining a new Lyapunov functional which contains a triple-integral term with the idea of decomposing the delay interval of time-varying delay, an improved criterion of asymptotic stability is derived in term of linear matrix inequalities. The criterion proves to be less conservative with fewer matrix variables than some previous ones. Finally, a numerical example is given to show the effectiveness of the proposed method.

scholarly journals Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jianting Zhou ◽  
Qiankun Song ◽  
Jianxi Yang
Keyword(s):  
Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Analysis Technique ◽  
Uncertain Neural Networks ◽  
Delay Dependent ◽  
Varying Delay

The passivity problem is investigated for a class of stochastic uncertain neural networks with time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibniz formulation, the free-weighting matrix method, and stochastic analysis technique, a delay-dependent criterion for checking the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example with simulation is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

New Criterion for Stability of Linear Systems with Interval Time-Varying Delay

2014 ◽  
Vol 651-653 ◽  
pp. 2339-2342
Author(s):  
Ting Ting Wang ◽  
Zhao Di Xu ◽  
Hong Su
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
New Criterion ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper is concerned with the delay-dependent stability for linear systems. Through constructing a new augmented LKF and using a new integral inequality, the improved delay-dependent stability criteria are derived in terms of linear matrix inequalities, and it is established that the results have less conservativ`e than some existing stability conditions. Finally, numerical examples are given to illustrate the effectiveness of the proposed result.

A Novel Stability Criterion of Lur’e Systems with Time-Varying Delay Based on Relaxed Conditions

2018 ◽  
Vol 30 (6) ◽  
pp. 965-970
Author(s):  
Peng Zhang ◽  
◽  
Pitao Wang ◽  
Tao Shen
Keyword(s):  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Decomposition Approach ◽  
Time Varying Delay ◽  
Delay Decomposition Approach ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper considers the absolute stability for Lur’e systems with time-varying delay and sector-bounded nonlinear. In this paper, a new relaxed condition based on delay decomposition approach is proposed. By using this technique and employing some inequality, the new delay-dependent stability criteria for Lur’e systems are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to show less conservatism of proposed methods compared with the previous.

scholarly journals Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1445
Author(s):  
Cheung-Chieh Ku ◽  
Wen-Jer Chang ◽  
Kuan-Wei Huang
Keyword(s):  
Fuzzy Systems ◽  
Multiplicative Noise ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

scholarly journals New Absolute Stability Conditions of Lur’e Systems with Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Wang ◽  
Hong-Bing Zeng
Keyword(s):  
Absolute Stability ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Lur’E Systems ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
The Relationship ◽  
Varying Delay

This paper is focused on the absolute stability of Lur’e systems with time-varying delay. Based on the quadratic separation framework, a complete delay-decomposing Lyapunov-Krasovskii functional is constructed. By considering the relationship between the time-varying delay and its varying interval, improved delay-dependent absolute stability conditions in terms of linear matrix inequalities (LMIs) are obtained. Moreover, the derived conditions are extended to systems with time-varying structured uncertainties. Finally, a numerical example is given to show the advantage over existing literatures.

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