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 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 Guaranteed Cost Finite-Time Control of Discrete-Time Positive Impulsive Switched Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Time Control ◽  
Guaranteed Cost ◽  
Impulsive Switched Systems ◽  
Finite Time Boundedness ◽  
Definition Of

This paper considers the guaranteed cost finite-time boundedness of discrete-time positive impulsive switched systems. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the multiple linear copositive Lyapunov function (MLCLF) and average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are obtained to guarantee that the corresponding closed-loop system is guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

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 Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Feedback Controller ◽  
Closed Loop Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Positive Switched Systems

The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS) is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.

scholarly journals Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems

2019 ◽  
Vol 17 (1) ◽  
pp. 716-727
Author(s):  
Leipo Liu ◽  
Hao Xing ◽  
Xiangyang Cao ◽  
Xiushan Cai ◽  
Zhumu Fu
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Actual State ◽  
Time Control ◽  
Guaranteed Cost ◽  
Impulsive Switched Systems ◽  
Positive Observer

Abstract This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Observer-based H∞ finite-time control for switched linear systems with interval time-delay

2018 ◽  
Vol 41 (5) ◽  
pp. 1348-1360 ◽  
Author(s):  
Gökhan Göksu ◽  
Ulviye Başer
Keyword(s):  
Time Delay ◽  
Finite Time ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linearization Method ◽  
Interval Time ◽  
Time Control ◽  
Finite Time Boundedness ◽  
Time Bounds

In this work, interval time-delay switched systems having completely unstable and mixed stable matrices of the state vector are considered. An observer-based controller is designed for finite-time boundedness and H∞-control of these systems. New sufficient conditions on the existence of a desired observer are developed and new average dwell-time bounds are introduced separately in case of unstable and mixed stable subsystems. An algorithm is presented for the calculation of unknown constants in the average dwell-time bounds which depend on nonlinear matrices in terms of the cone complementarity linearization method. Finally, numerical examples are given for the effectiveness and validity of the proposed solutions.

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 Robust Finite-TimeH∞Control for Impulsive Switched Nonlinear Systems with State Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jian Guo ◽  
Chao Liu ◽  
Zhengrong Xiang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
State Delay ◽  
Impulsive Switched Systems ◽  
Finite Time Boundedness ◽  
Impulsive Switched System

This paper investigates robust finite-timeH∞control for a class of impulsive switched nonlinear systems with time-delay. Firstly, using piecewise Lyapunov function, sufficient conditions ensuring finite-time boundedness of the impulsive switched system are derived. Then, finite-timeH∞performance analysis for impulsive switched systems is developed, and a robust finite-timeH∞state feedback controller is proposed to guarantee that the resulting closed-loop system is finite-time bounded withH∞disturbance attenuation. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show 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.

Finite-time boundedness and stabilization of switched nonlinear systems using auxiliary matrices and average dwell time method

2019 ◽  
Vol 42 (7) ◽  
pp. 1406-1416 ◽  
Author(s):  
Hadi Gholami ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
System Matrix ◽  
Lyapunov Matrix ◽  
Average Dwell Time Method ◽  
Finite Time Boundedness

This paper focuses on the finite-time boundedness of switched nonlinear systems based on the Finsler’s lemma, auxiliary matrices, and average dwell time method. The analysis is provided for a switched system with Lipschitz nonlinearities and in the presence of external disturbances. Moreover, a switching controller is designed based on linear matrix inequalities (LMIs), to make the closed-loop system finite-time bounded. Presented theorems in this paper are more general and have less conservatism than the existing methods due to using the auxiliary matrices that make the Lyapunov matrix separate from the system matrix in the resulting LMIs. Moreover, in all theorems, the average dwell time of the switching system has been evaluated. Three examples are given to illustrate the effectiveness of the proposed method and to show that it is less conservative compared with existing methods.

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