Adaptive finite-time control for non-linear delay systems via non-fragile state feedback

2015 ◽  
Vol 39 (5) ◽  
pp. 635-641 ◽  
Author(s):  
Yitao Yang ◽  
Linlin Hou ◽  
Haibin Sun
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Delay Systems ◽  
Time Stability ◽  
Fragile State ◽  
Finite Time Stability ◽  
Time Control ◽  
Linear Delay ◽  
Non Linear ◽  
Finite Time Boundedness

The problem of adaptive finite-time control is addressed in this paper for a class of non-linear delay systems. First, the concepts of adaptive finite-time stability and adaptive finite-time boundedness are defined, respectively. Then, by resorting to the Lyapunov–Krasovskii functional technique, some new delay-dependent criteria guaranteeing adaptive finite-time boundedness and adaptive finite-time stability are developed, respectively. An explicit expression for the desired non-fragile state feedback controller is also presented. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.

scholarly journals Finite-Time Boundedness Control of Time-Varying Descriptor Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiaoming Su ◽  
Yali Zhi ◽  
Qingling Zhang
Keyword(s):  
Control Problem ◽  
Finite Time ◽  
State Feedback ◽  
Descriptor Systems ◽  
Necessary Condition ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness ◽  
Sufficient And Necessary Condition

This paper mainly studies a control problem of finite-time boundedness of time-varying descriptor systems. Firstly, a sufficient and necessary condition of finite-time stability is given, then a sufficient condition of finite-time boundedness for time-varying descriptor systems is given. Secondly, we analyze the finite-time boundedness control problem and design the finite-time state feedback controller; the controller is given based on LMIs for time-varying descriptor systems and time-varying uncertain descriptor systems, respectively. Finally, a numerical example is given to prove the effectiveness of the method.

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

Finite-time stability and finite-time boundedness of fractional order switched systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3364-3371 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Lili Liu ◽  
Yue-E Wang ◽  
Changtao Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability and finite-time boundedness of fractional order switched systems with [Formula: see text] are investigated in this paper. First of all, by employing the average dwell time technique and Lyapunov functional method, some sufficient conditions for finite-time stability and finite-time boundedness of fractional order switched systems are proposed. Furthermore, the state feedback controllers are constructed, and sufficient conditions are given to ensure that the corresponding closed-loop systems are finite-time stable and finite-time bounded. These conditions can be easily obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness of the results.

Finite-Time H∞ Control of one Family of Fuzzy Discrete-Time System with Norm-Bounded Disturbance

2011 ◽  
Vol 225-226 ◽  
pp. 428-432 ◽  
Author(s):  
Cai Xia Liu ◽  
Ying Qi Zhang
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Function Theory ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Discrete Time System ◽  
Time System ◽  
Finite Time Stability ◽  
Time Control ◽  
Bounded Disturbance

This paper deals with finite-time control problem of a class of fuzzy discrete-time system with time-varying norm-bounded disturbance. Applying the Lyapunov function theory and matrix inequalities, a sufficient condition is obtained for robust finite-time stability and the fuzzy system satisfies a prescribed level for the effect of the disturbance input on the controlled output.

scholarly journals Finite-Time Stability Analysis for a Class of Continuous Switched Descriptor Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pan Tinglong ◽  
Yang Kun ◽  
Shen Yanxia ◽  
Gao Zairui ◽  
Ji Zhicheng
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Interval ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability has more practical application values than the classical Lyapunov asymptotic stability over a fixed finite-time interval. The problems of finite-time stability and finite-time boundedness for a class of continuous switched descriptor systems are considered in this paper. Based on the average dwell time approach and the multiple Lyapunov functions technique, the concepts of finite-time stability and boundedness are extended to continuous switched descriptor systems. In addition, sufficient conditions for the existence of state feedback controllers in terms of linear matrix inequalities (LMIs) are obtained with arbitrary switching rules, which guarantee that the switched descriptor system is finite-time stable and finite-time bounded, respectively. Finally, two numerical examples are presented to illustrate the reasonableness and effectiveness of the proposed results.

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