scholarly journals New Results on Stability and Stabilization of Markovian Jump Systems with Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongwei Xia ◽  
Li Li ◽  
Yanmin Wang ◽  
Guangcheng Ma ◽  
Changhong Wang
Keyword(s):  
Stochastic Stability ◽  
Delay Systems ◽  
Closed Loop System ◽  
Markovian Jumping ◽  
Time Varying Delay ◽  
Markovian Jumping Systems ◽  
Stability And Stabilization ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.

scholarly journals Delay-DependentH∞Control for Descriptor Markovian Jump Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Jinghao Li ◽  
Qingling Zhang ◽  
Ding Zhai ◽  
Yi Zhang
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This paper is concerned with the delay-dependentH∞control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribedH∞performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

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.

Fault-Distribution Dependent Reliable H∞ Control for Takagi-Sugeno Fuzzy Systems

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
R. Sakthivel ◽  
P. Vadivel ◽  
K. Mathiyalagan ◽  
A. Arunkumar
Keyword(s):  
Fuzzy Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Actuator Failure ◽  
Time Varying Delay ◽  
Actuator Failures ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay

This paper is concerned with the problem of robust reliable H∞ control for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H∞ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H∞ performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMIs for the existence of robust reliable H∞ controller. When these LMIs are feasible, a robust reliable H∞ controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.

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