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 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 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 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 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 Finite-time stabilization of switched linear systems and its application in terminal guidance

2016 ◽  
Vol 13 (6) ◽  
pp. 172988141667980
Author(s):  
Yang Guo ◽  
Xiaoxiang Hu ◽  
Biao Deng ◽  
Shuai Zhang ◽  
Yu Jiang
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
State Feedback ◽  
State Constraints ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Finite Time Stabilization ◽  
Finite Time Boundedness ◽  
Terminal Guidance

This article presents finite-time stabilization methods of switched linear systems with disturbances. After extending finite-time stabilization and finite-time boundedness definitions to switched linear systems, sufficient conditions guaranteeing system finite-time boundedness are proposed, by which the state feedback controller method is obtained. For a class of switched terminal guidance systems, the methods are illustrated by application to guidance design to solve the finite-time stabilization problem considering nonzero initial conditions and state constraints.

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 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.

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