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 Input-to-State Stability and Optimization of Switched Nonlinear Systems

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Xiaoli Wang ◽  
Chuntao Shao
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Stability Problem ◽  
Stability Property ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Time Switching ◽  
Switched Nonlinear System ◽  
Average Dwell Time Switching

In this paper, we address the (uniform) finite-time input-to-state stability problem for switched nonlinear systems. We prove that a switched nonlinear system has a useful finite-time input-to-state stability property under average dwell-time switching signals if each constituent subsystem has finite-time input-to-state stability. Moreover, we prove the equivalence between the optimal costs for the switched nonlinear systems and for the relaxed differential inclusion.

scholarly journals Finite-Time Formation of Unmanned Aerial Vehicles with Switching Topologies and Disturbances: An Average Dwell Time Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Chao Ma ◽  
Wei Wu
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Finite Time ◽  
Dwell Time ◽  
Average Dwell Time ◽  
Time Stability ◽  
External Disturbances ◽  
Finite Time Stability ◽  
Switching Topologies ◽  
Aerial Vehicles ◽  
Formation Problem

This paper investigates the finite-time formation problem of unmanned aerial vehicles (UAVs) with switching topologies and external disturbances. The formation problem is first transformed into the finite-time stability and bounded problems of a switched system, respectively. In particular, the finite-time unachievable topology is concerned for unreliable information exchanges. By employing the average dwell time (ADT) method, sufficient criteria are established to deal with the switching topologies such that the desired time-varying formation can be achieved in finite time. Then, the topology-dependent controller can be designed in terms of matrix technique. Finally, an illustrative example is given to verify the effectiveness of our proposed formation strategy.

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 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.

Sign in / Sign up

Export Citation Format

Share Document