scholarly journals L1 Input-Output Finite-Time Control of Positive Switched Nonlinear Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Bo Fan ◽  
Zhumu Fu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Distributed Delays ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Input Output ◽  
Positive Type ◽  
Time Control

In this paper, the problem of L1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated. Nonlinear functions considered in this paper are located in a sector field. Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L1 input-output finite-time stability (L1 IO-FTS) is firstly introduced. Then, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L1 IO-FTS. Such conditions can be easily solved by linear programming. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

scholarly journals Input-Output Finite-Time Control of Positive Switched Systems with Time-Varying and Distributed Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Distributed Delays ◽  
Time Varying ◽  
Input Output ◽  
Finite Time Stability ◽  
Time Control ◽  
Positive Switched Systems

The problem of input-output finite-time control of positive switched systems with time-varying and distributed delays is considered in this paper. Firstly, the definition of input-output finite-time stability is extended to positive switched systems with time-varying and distributed delays, and the proof of the positivity of such systems is also given. Then, by constructing multiple linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a state feedback controller is designed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is input-output finite-time stable (IO-FTS). Such conditions can be easily solved by linear programming. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

2017 ◽  
Vol 15 (1) ◽  
pp. 1635-1648 ◽  
Author(s):  
Hao Xing ◽  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Finite Time Boundedness

Abstract This paper considers the guaranteed cost finite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and sufficient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the effectiveness of the proposed method.

scholarly journals Exponential Stability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays via an Average Dwell-Time Method

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
N. Yotha ◽  
T. Botmart ◽  
T. Mouktonglang
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Fast Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Unstable Subsystems

The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness 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 Disturbance Observer-Based Input-Output Finite-Time Control of a Class of Nonlinear Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Leipo Liu ◽  
Xiaona Song ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Disturbance Observer ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Law ◽  
Input Output ◽  
Classical State ◽  
Time Control

This paper is concerned with disturbance observer-based input-output finite-time control of a class of nonlinear systems with one-sided Lipschitz condition, as well as multiple disturbances. Firstly, a disturbance observer is constructed to estimate the disturbance generated by an exogenous system. Secondly, by integrating the estimation of disturbance with a classical state feedback control law, a composite control law is designed and sufficient conditions for input-output finite-time stability (IO-FTS) of the closed-loop system are attained. Such conditions can be converted into linear matrix inequalities (LMIs). Finally, two examples are given to show the effectiveness of the proposed method.

Finite-time stability and asynchronously switching control for a class of time-varying switched nonlinear systems

2019 ◽  
Vol 42 (6) ◽  
pp. 1215-1224
Author(s):  
Ronghao Wang ◽  
Jianchun Xing ◽  
Zhengrong Xiang ◽  
Qiliang Yang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Dwell Time ◽  
Autonomous Systems ◽  
Average Dwell Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Control Lyapunov Function ◽  
Finite Time Stability

Finite-time stability and stabilization for switched nonlinear systems has been investigated in the paper. Based on existing works, we find that related results on autonomous switched nonlinear systems cannot be simply extended to non-autonomous systems. A sufficient condition has been proposed for this class of systems using the average dwell time method. Specifically, a control Lyapunov function approach is employed to stabilize the system and the finite-time controller is designed using a small control property. In contrast to autonomous switched systems, a finite-time stabilizer is constructed for time-varying switched nonlinear systems, even under the situation in which the switching mode is different between the system and the controller. Furthermore, the relation between the settling time and the average dwell time has been revealed. Finally, an example case is presented for the obtained result.

Asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems

2019 ◽  
Vol 41 (14) ◽  
pp. 4157-4166 ◽  
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Yifan Di
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Input Output ◽  
Finite Time Stability ◽  
Time Control ◽  
Positive Switched Systems

This paper considers asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems (DNIPSS). Firstly, the definition of input-output finite-time stability (IO-FTS) is introduced. By using the linear co-positive Lyapunov function (LCLF) and average dwell time (ADT) approach, a state feedback controller via asynchronous switching is designed and sufficient conditions are obtained to guarantee the corresponding closed-loop system is IO-FTS. Such conditions can be solved by linear programming. Furthermore, the mode-dependent average dwell time (MDADT) method for asynchronously input-output finite-time control of DNIPSS is also presented. Finally, two examples are provided to show the effectiveness of the proposed method.

scholarly journals Neural networks-based adaptive finite-time control of switched nonlinear systems under time-varying actuator failures

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xikui Liu ◽  
Xiurong Shi ◽  
Yan Li
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Fault Tolerant ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Actuator Failures ◽  
Time Control

AbstractThis paper is dedicated to neural networks-based adaptive finite-time control design of switched nonlinear systems in the time-varying domain. More specifically, by employing the approximation ability of neural networks system, an integrated adaptive controller is constructed. The main aim is to make sure the closed-loop system in arbitrary switching signals is semi-global practical finite-time stable (SGPFS). A backstepping design with a common Lyapunov function is proposed. Unlike some existing control schemes with actuator failures, the key is dealing with the time-varying fault-tolerant job for the switched system. It is also proved that all signals in the system are bounded and the tracking error can converge in a small field of the origin in finite time. A practical example is presented to illustrate the validity of the theory.

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