scholarly journals On Finite-Time Stability of Switched Systems with Hybrid Homogeneous Degrees

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bin Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Nonlinear Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Numerical Example

The finite-time stability is investigated for switched nonlinear systems. It is assumed that each subsystem possesses a positive homogeneous Lyapunov-like function. The derivative of the function is with hybrid homogenous degrees. Three substantially different situations are considered and different sufficient conditions are provided, respectively. The utility of our result is illustrated through the study of a numerical example.

Finite-time stability and finite-time boundedness of fractional order switched systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3364-3371 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Lili Liu ◽  
Yue-E Wang ◽  
Changtao Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability and finite-time boundedness of fractional order switched systems with [Formula: see text] are investigated in this paper. First of all, by employing the average dwell time technique and Lyapunov functional method, some sufficient conditions for finite-time stability and finite-time boundedness of fractional order switched systems are proposed. Furthermore, the state feedback controllers are constructed, and sufficient conditions are given to ensure that the corresponding closed-loop systems are finite-time stable and finite-time bounded. These conditions can be easily obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness of the results.

scholarly journals Finite-time stability of multiterm fractional nonlinear systems with multistate time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
G. Arthi ◽  
N. Brindha ◽  
Yong-Ki Ma
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
The Novel ◽  
Finite Range ◽  
Time Stability ◽  
Finite Time Stability ◽  
Fractional System ◽  
The Stability

AbstractThis work is mainly concentrated on finite-time stability of multiterm fractional system for $0 < \alpha _{2} \leq 1 < \alpha _{1} \leq 2$ 0 < α 2 ≤ 1 < α 1 ≤ 2 with multistate time delay. Considering the Caputo derivative and generalized Gronwall inequality, we formulate the novel sufficient conditions such that the multiterm nonlinear fractional system is finite time stable. Further, we extend the result of stability in the finite range of time to the multiterm fractional integro-differential system with multistate time delay for the same order by obtaining some inequality using the Gronwall approach. Finally, from the examples, the advantage of presented scheme can guarantee the stability in the finite range of time of considered systems.

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.

Finite-time H∞ dynamic quantization inputs control for uncertain switched systems

2020 ◽  
pp. 014233122093342
Author(s):  
Liangda Zhang ◽  
Baowei Wu ◽  
Lili Liu
Keyword(s):  
Lipschitz Condition ◽  
Finite Time ◽  
Switched Systems ◽  
Lipschitz Constant ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Time Stability ◽  
Finite Time Stability ◽  
Nonlinear Disturbances

This paper investigates the problem of finite-time stability and finite-time [Formula: see text] stabilization for switched systems with parametric uncertainties and nonlinear disturbances satisfying Lipschitz condition. The dynamic quantization inputs feedback control technology is proposed to utilize quantized input measurements which can significantly reduce the communication burden. Sufficient conditions in terms of linear matrix inequality (LMIs) are presented through applying Lyapunov function method and average dwell approach to ensure the finite-time stability of the switched system. By analysing the feasibility of LMIs’ solution, the feedback gain matrix and the dynamic quantization parameter are obtained. In addition, more constraints are proposed to ensure the finite-time stabilization with a prescribed [Formula: see text] performance index with respect to nonlinear disturbances, and the Lipschitz constant matrix of Lipschitz condition is not required to be known in advance. Finally, with the application to the proposed control of a numerical example and a two-stage chemical reactor system, the validity of the conclusion is verified.

scholarly journals Finite-Time Optimization Stabilization for a Class of Constrained Switched Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Baili Su ◽  
Dandan Chunyu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Switched Nonlinear Systems ◽  
Region Of Attraction ◽  
Time Stability ◽  
Finite Time Stability ◽  
System A ◽  
Time Optimization ◽  
Switched Nonlinear System ◽  
And Control

This paper studies the finite-time stability problem of a class of switched nonlinear systems with state constraints and control constrains. For each subsystem, optimization controller is designed by choosing the appropriate Lyapunov function to stabilize the subsystem in finite time and the estimation of the region of attraction can be prescribed. For the whole switched nonlinear system, a suitable switched law is designed to ensure the following: (1) at the time of the transition, Lyapunov function’s value of the switched-in subsystem being less than the value of the last subsystem; (2) the finite-time stability of the whole close-loop system. Finally, a simulation example is used to verify the effectiveness of the proposed algorithm.

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