Optimized state-dependent switching law design for a class of switched nonlinear systems with two unstable subsystems

2021 ◽  
Vol 397 ◽  
pp. 125872
Author(s):  
Yusheng Zhou ◽  
Danhong Chen
Keyword(s):  
Nonlinear Systems ◽  
Switched Nonlinear Systems ◽  
Switching Law ◽  
Unstable Subsystems ◽  
State Dependent

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

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.

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.

Switched nonlinear systems with state-dependent dwell-time

2003 ◽  
Vol 50 (4) ◽  
pp. 291-302 ◽  
Author(s):  
Claudio De Persis ◽  
Raffaella De Santis ◽  
A.Stephen Morse
Keyword(s):  
Nonlinear Systems ◽  
Dwell Time ◽  
Switched Nonlinear Systems ◽  
State Dependent

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 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.

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