Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Jun-Wei Wang ◽  
Huai-Ning Wu ◽  
Yue-Sheng Luo
Keyword(s):  
Stochastic Stability ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markov Jump ◽  
Lmi Optimization ◽  
Markov Jump Linear Systems ◽  
Linear Delay ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper studies the problem of robustly stochastic stability and stabilization for a class of uncertain Markov jump linear systems with time delay. A new stochastic Lyapunov–Krasovskii functional (LKF) is constructed for the stability analysis and stabilization, in which the delay is uniformly divided into multiple segments. Based on this LKF and using an improved Jensen's integral inequality, the improved delay-dependent stochastic stability criteria are first derived in terms of linear matrix inequalities (LMIs). Then, an LMI approach to the design of stabilizing controllers via delayed state feedback is developed. The previous stability criteria are extended to give the delay-dependent stabilization conditions in terms of LMIs. Furthermore, an LMI optimization algorithm is proposed to find the maximum allowable delay of the system. Finally, numerical examples show that the proposed results are effective and much less conservative than some existing results.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

scholarly journals LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

2012 ◽  
Vol 22 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Pagavathigounder Balasubramaniam ◽  
Shanmugam Lakshmanan ◽  
Rajan Rakkiyappan
Keyword(s):  
Robust Stability ◽  
Optimization Problem ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Lmi Optimization ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertaintiesThis paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

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