Robust Stabilization for a Class of Switched Nonlinear Systems

2012 ◽  
Vol 490-495 ◽  
pp. 1536-1540
Author(s):  
Cai Yun Wu ◽  
Ben Niu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
Closed Loop System ◽  
Multiple Lyapunov Functions ◽  
Switching Law ◽  
Nonlinear Part ◽  
State Dependent

This paper addresses the stabilization problem for a class of switched nonlinear systems with Lipschitz nonlinearities using the multiple Lyapunov functions (MLFs) approach. A state feedback controller and a state dependent switching law are proposed to asymptotic stabilization the switched system via linear matrix inequalities (LMI). The developed control strategy ensures asymptotic stability of the closed-loop system even if the nonlinear part . Finally, the feasibility of the proposed method is illustrated through a simulation example

scholarly journals Homogeneous Stabilizer by State Feedback for Switched Nonlinear Systems Using Multiple Lyapunov Functions’ Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Ye ◽  
Bin Jiang ◽  
Hao Yang
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Homogeneous State ◽  
Switched Nonlinear Systems ◽  
Multiple Lyapunov Functions ◽  
Globally Asymptotically Stable ◽  
Switching Law ◽  
Adding A Power Integrator ◽  
Linear Growth Condition

This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs). The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.

Incremental passivity and stabilization for switched nonlinear systems

2020 ◽  
Vol 42 (11) ◽  
pp. 2088-2102
Author(s):  
Hongbo Pang ◽  
Chensong Li
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Energy Change ◽  
Relative Degree ◽  
Switched Nonlinear Systems ◽  
Feedback Controllers ◽  
Switching Law ◽  
State Dependent ◽  
Switched Nonlinear System

This paper studies the problems of incremental passivity, incremental passification and incremental stabilization for a switched nonlinear system. First, an incremental passivity concept for switched nonlinear systems is proposed. Each subsystem is only required to be incrementally passive, when it is active. The energy change of each inactive subsystem is charaterized. Then, a sufficient condition for such a system to be incrementally passive is given. Second, a state-dependent switching law and state feedback controllers are designed to render a system with relative degree one incrementally passive. Third, we show that an incrementally passive switched nonlinear system can be incrementally stabilized under some constraints on the energy change of inactive subsystems. In particular, a recursive feedback incremental passification design technique is adopted to achieve the incremental stability for a switched nonlinear system with any same relative degree by designing a set of feedback controllers and a state-dependent switching law, constructively. Finally, two examples are provided to verify the effectiveness of the proposed theory.

scholarly journals Robust Reliable Stabilization of Switched Nonlinear Systems with Time-Varying Delays and Delayed Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Zhengrong Xiang ◽  
Qingwei Chen
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Actuator Failure ◽  
Exponentially Stable

This paper is concerned with the problem of robust reliable stabilization of switched nonlinear systems with time-varying delays and delayed switching is investigated. The parameter uncertainties are allowed to be norm-bounded. The switching instants of the controller experience delays with respect to those of the system. The purpose of this problem is to design a reliable state feedback controller such that, for all admissible parameter uncertainties and actuator failure, the system state of the closed-loop system is exponentially stable. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of linear matrix inequalities (LMIs).

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

scholarly journals Robust H1 control for a class of switched nonlinear systems

2016 ◽  
Vol 12 (2) ◽  
pp. 5870-5879
Author(s):  
Hui Xu ◽  
Min Wang
Keyword(s):  
Nonlinear Systems ◽  
Control Problem ◽  
Closed Loop ◽  
Average Dwell Time ◽  
Control Law ◽  
Switched Nonlinear Systems ◽  
Switching Law ◽  
Nonlinear Part ◽  
Exponentially Stable ◽  
Average Dwell Time Method

This article is concerned with the robust H1 control problem of a class of switched nonlinear systems with norm-bounded time-varying uncertainties. The system considered in this class is composed of two parts: a uncertain linear switched part and a nonlinear part, which is also switched systems. Under the circumstances, that the H1 control problem of all subsystems are not all solvable, the switched feedback control law and the switching law are designed using the average dwell-time method. The corresponding closed-loop switched system is exponentially stable and achieves a weighted L2-gain.

Guaranteed Cost Control for a Class of Switched Descriptor Systems

2012 ◽  
Vol 546-547 ◽  
pp. 1030-1034
Author(s):  
Chun Yuan Zhao ◽  
Shu Hui Shi
Keyword(s):  
State Feedback ◽  
Cost Control ◽  
Convex Combination ◽  
Guaranteed Cost Control ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Combination Technique ◽  
Switching Law ◽  
Guaranteed Cost

This paper deals with the problem of guaranteed cost control for a class of switched descriptor systems. State feedback guaranteed cost controller is adopted to make the resulting closed-loop system stable and cost function have an upper bound. Based on single Lyapunov function and convex combination technique, a switching law is designed and a sufficient condition of the existence of such controller is presented. By means of variables substitution and linear matrix inequality, the condition can be turned to LMI. The advantage of method presented in this paper is illustrated by an example.

Incremental passivity-based H∞ output tracking control for switched nonlinear systems

2019 ◽  
Vol 41 (13) ◽  
pp. 3600-3611
Author(s):  
Shuo Liu ◽  
Hongbo Pang ◽  
Chensong Li
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Switched System ◽  
Switched Nonlinear Systems ◽  
Feedback Controllers ◽  
External Disturbances ◽  
Switching Law ◽  
Output Tracking ◽  
Output Tracking Control ◽  
State Dependent

This paper is concerned with the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances using incremental passivity, even if the problem of H∞ output tracking control for none of subsystems is solvable. First, an incremental passivity concept of switched nonlinear systems without external disturbances is proposed. This incremental passivity property requires each active subsystem is incrementally passive. Then, sufficient conditions to be incrementally passive are given. Second, by resorting to the established incremental passivity theory, a state-dependent switching law and a set of feedback controllers are designed to solve the problem of H∞ output tracking control for a class of switched nonlinear systems with external disturbances. This avoids solving Hamilton-Jacobi (HJ) inequality. Third, a composite state-dependent switching law and the state feedback controllers are designed to solve the H∞ output tracking problem for a class of cascaded switched nonlinear systems with external disturbances. The designed composite switching law allows the driven switched system and the driving switched system switch asynchronously. Finally, two examples are provided to verify the effectiveness of the proposed method.

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