scholarly journals On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yingqi Zhang ◽  
Caixia Liu ◽  
Xiaowu Mu
Keyword(s):  
Discrete Time ◽  
Packet Loss ◽  
Finite Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Packet Dropout ◽  
Model Description ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.

scholarly journals Stochasticℋ∞Finite-Time Control of Discrete-Time Systems with Packet Loss

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yingqi Zhang ◽  
Wei Cheng ◽  
Xiaowu Mu ◽  
Caixia Liu
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Packet Loss ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Model Description ◽  
Discrete Time Systems ◽  
Finite Time Stabilization ◽  
Finite Time Boundedness ◽  
Time Systems

This paper investigates the stochastic finite-time stabilization andℋ∞control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochasticℋ∞finite-time boundedness and then state feedback controllers are designed to guarantee stochasticℋ∞finite-time stabilization of the class of stochastic systems. The stochasticℋ∞finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.

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.

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.

scholarly journals H_∞ Finite-time Boundedness for Discrete-time Delay Neural Networks via Reciprocally Convex Approach

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Le Anh Tuan
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Discrete Time Delay ◽  
Finite Time Boundedness ◽  
Reciprocally Convex Approach

This paper addresses the problem of finite-time boundedness for discrete-time neural networks with interval-like time-varying delays. First, a delay-dependent finite-time boundedness criterion under the finite-time  performance index for the system is given based on constructing a set of adjusted Lyapunov–Krasovskii functionals and using reciprocally convex approach. Next, a sufficient condition is drawn directly which ensures the finite-time stability of the corresponding nominal system. Finally, numerical examples are provided to illustrate the validity and applicability of the presented conditions. Keywords: Discrete-time neural networks,  performance, finite-time stability, time-varying delay, linear matrix inequality.  

scholarly journals Finite-Time Stability and Stabilization of Networked Control Systems with Bounded Markovian Packet Dropout

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Yeguo Sun ◽  
Guanjun Li
Keyword(s):  
Control Systems ◽  
Finite Time ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Time Stability ◽  
Finite Time Stability ◽  
Stability And Stabilization

The finite-time stability and stabilization problems of a class of networked control systems (NCSs) with bounded Markovian packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time stability and stabilization via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump linear systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time stability and stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

scholarly journals Finite-Time Boundedness and Stabilization of Networked Control Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yeguo Sun ◽  
Jin Xu
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Finite Time ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

The finite-time control problem of a class of networked control systems (NCSs) with time delay is investigated. The main results provided in the paper are sufficient conditions for finite-time stability via state feedback. An augmentation approach is proposed to model NCSs with time delay as linear systems. Based on finite time stability theory, the sufficient conditions for finite-time boundedness and stabilization of the underlying systems are derived via linear matrix inequalities (LMIs) formulation. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

scholarly journals Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays

2021 ◽  
Vol 17 ◽  
pp. 146-155
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

scholarly journals Finite-Time Stability Analysis and Control for a Class of Stochastic Singular Biological Economic Systems Based on T-S Fuzzy Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shuangyun Xing ◽  
Qingling Zhang ◽  
Yi Zhang
Keyword(s):  
Finite Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Economic Systems ◽  
Time Stability ◽  
Control Approach ◽  
Finite Time Stability ◽  
Stability And Control ◽  
And Control

This paper studies the problem of finite-time stability and control for a class of stochastic singular biological economic systems. It shows that such systems exhibit the distinct dynamic behavior when the economic profit is a variable rather than a constant. Firstly, the stochastic singular biological economic systems are established as fuzzy models based on T-S fuzzy control approach. These models are described by stochastic singular T-S fuzzy systems. Then, novel sufficient conditions of finite-time stability are obtained for the stochastic singular biological economic systems, and the state feedback controller is designed so that the population (state of the systems) can be driven to the bounded range by the management of the open resource. Finally, by using Matlab software, numerical examples are given to illustrate the effectiveness of the obtained results.

scholarly journals New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten B. Stojanovic
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

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