scholarly journals Finite-Time Boundedness Analysis for a Class of Switched Linear Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Time Varying ◽  
Switched Linear Systems ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

The problem of finite-time boundedness for a class of switched linear systems with time-varying delay and external disturbance is investigated. First of all, the multiply Lyapunov function of the system is constructed. Then, based on the Jensen inequality approach and the average dwell time method, the sufficient conditions which guarantee the system is finite-time bounded are given. Finally, an example is employed to verify the validity of the proposed method.

scholarly journals Guaranteed Cost Finite-Time Control for Positive Switched Linear Systems with Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Xiangyang Cao ◽  
Leipo Liu ◽  
Zhumu Fu ◽  
Xiaona Song ◽  
Shuzhong Song
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
State Feedback Control ◽  
Time Varying ◽  
Switched Linear Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Finite Time Boundedness

This paper considers the guaranteed cost finite-time control for positive switched linear systems with time-varying delays. The definition of guaranteed cost finite-time boundedness is firstly given. Then, by using the mode-dependent average dwell time approach, a static output feedback law and a state feedback control law are constructed, respectively, and sufficient conditions are obtained to guarantee that the closed-loop system is guaranteed cost finite-time boundedness. Such conditions can be easily solved by linear programming. Finally, an example is given to illustrate the effectiveness of the proposed method.

scholarly journals Observer-Based Event-Triggered Control for Switched Systems with Time-Varying Delay and Norm-Bounded Disturbance

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Guoqi Ma ◽  
Linlin Qin ◽  
Xinghua Liu ◽  
Gang Wu
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Varying ◽  
Time Varying Delay ◽  
Exogenous Disturbance ◽  
Finite Time Stabilization ◽  
Finite Time Boundedness ◽  
Varying Delay ◽  
Event Triggered

This paper is concerned with the problem of observed-based event-triggered control for switched linear systems with time-varying delay and exogenous disturbance. First by employing a state observer, an observer-based event-triggered controller is designed to guarantee the finite-time boundedness and finite-time stabilization of the resulting dynamic augmented closed-loop system. Then based on the Lyapunov-like function method and the average dwell time technique, some sufficient conditions are given to ensure the finite-time boundedness and finite-time stabilization, respectively. Furthermore, the lower bound of the minimum interevent interval is proved to be positive, which thus excludes the Zeno behavior of sampling. A numerical example is finally exploited to verify the effectiveness and potential of the achieved control scheme.

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 Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 713 ◽  
Author(s):  
Chanikan Emharuethai ◽  
Piyapong Niamsup ◽  
Raja Ramachandran ◽  
Wajaree Weera
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

scholarly journals Finite-time Stabilization for Uncertain Neural Networks With Time-varying Delay

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Control Design ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Neural Networks ◽  
Finite Time Boundedness ◽  
And Control ◽  
Varying Delay

In this paper, the problems of finite-time boundedness and control design for uncertain neuralnetworks with time-varying delay is considered. By constructing Lyapunov-Krasovskii function and using thematrix inequality method, sufficient conditions for finite-time boundedness of a class of neural networks withtime-varying delay are established. Then, we proposed a criterion to ensure that the neural networks with timevarying delay is finite-time stabilizable. A numerical example is given to verify the validity of the results.

scholarly journals Finite-Timel1-Gain Control for Positive Switched Systems with Time-Varying Delay via Delta Operator Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shuo Li ◽  
Zhengrong Xiang ◽  
Hamid Reza Karimi
Keyword(s):  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Gain Control ◽  
Delta Operator ◽  
Time Varying ◽  
Operator Approach ◽  
Time Varying Delay ◽  
Positive Switched Systems ◽  
Varying Delay

This paper is concerned with the problem of finite-timel1-gain control for positive switched systems with time-varying delay via delta operator approach. Firstly, sufficient conditions which can guarantee thel1-gain finite-time boundedness of the underlying system are given by using the average dwell time approach and constructing an appropriate copositive type Lyapunov-Krasovskii functional in delta domain. Moreover, the obtained conditions can unify some previously suggested relevant results seen in literature of both continuous and discrete systems into the delta operator framework. Then, based on the results obtained, a state feedback controller is designed to ensure that the resulting closed-loop system is finite-time bounded with anl1-gain performance. Finally, a numerical example is presented to demonstrate the effectiveness and feasibility of the proposed method.

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