Fixed-time stability of positive nonlinear systems

2020 ◽  
Vol 42 (15) ◽  
pp. 2951-2955
Author(s):  
Yunru Zhu ◽  
Yuanshi Zheng ◽  
Xingwen Liu ◽  
Huaizhu Wang
Keyword(s):  
Nonlinear Systems ◽  
Stability Problem ◽  
Vector Fields ◽  
Lyapunov Method ◽  
Fixed Time ◽  
Sufficient Condition ◽  
Time Stability ◽  
Arbitrary Switching

This paper studies the fixed-time stability problem for positive nonlinear systems defined by cooperative vector fields. A criterion is derived to ensure fixed-time stabilization of the positive nonlinear systems using Lyapunov method. In addition, a sufficient condition is also presented for fixed-time stability of switched positive nonlinear systems under arbitrary switching. Simulation examples are provided to demonstrate the obtained results.

Fixed-time stability theorem of stochastic nonlinear systems

2018 ◽  
Vol 92 (9) ◽  
pp. 2194-2200 ◽  
Author(s):  
Jiaju Yu ◽  
Shuanghe Yu ◽  
Juan Li ◽  
Yan Yan
Keyword(s):  
Nonlinear Systems ◽  
Fixed Time ◽  
Stability Theorem ◽  
Stochastic Nonlinear Systems ◽  
Time Stability

Observer Design for Lipschitz Nonlinear Systems with Output Uncertainty

2014 ◽  
Vol 533 ◽  
pp. 277-280
Author(s):  
Wei Zou ◽  
Yu Sheng Liu ◽  
Kai Liu
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Observer Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Output Uncertainty ◽  
Lipschitz Nonlinear Systems ◽  
Simulation Results

This paper presents an observer design for Lipschitz nonlinear systems with output uncertainty. By means of Lyapunov method as well as linear matrix inequality (LMI), the observer gain matrix is determined and a sufficient condition ensuring the asymptotic stability of the observer is proposed. Simulation results demonstrate the robustness of the proposed observer for output uncertainty.

Sub-fixed-time control for a class of second order system

2020 ◽  
pp. 014233122092100
Author(s):  
Boyan Jiang ◽  
Hua Chen ◽  
Bo Li ◽  
Xuewu Zhang
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
Time Stability ◽  
Time Control ◽  
Initial States ◽  
The Stability

In this paper, a new concept “sub-fixed-time stability” (SFTS) is proposed and studied, which means the states can converge to a region of equilibrium points in a fixed time for any initial states’ values. Then, a sufficient condition for it is given and proven. Though SFTS is similar to “practical fixed-time stability” (PFTS), they are not the same, and the sufficient condition for SFTS is much clearer and simpler than PFTS. Next, a sub-fixed-time controller is proposed for a class of second order system. The stability analyses are given in the case without disturbance and with disturbance, respectively. Finally, to illustrate the robustness of the proposed sub-fixed-time controller to different initial conditions, 100 numerical simulations are conducted for 100 initial states’ values.

Finite-Time Stability for Continuous-Time Linear Singular Systems

2013 ◽  
Vol 846-847 ◽  
pp. 383-387
Author(s):  
Song Lin Wo ◽  
Xiao Xin Han
Keyword(s):  
Continuous Time ◽  
Finite Time ◽  
Stability Problem ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Linear

In this paper the finite-time stability (FST) problem of continuous-time linear singular systems (CTLSS) is considered. The main results provided are a sufficient condition of FTS for CTLSS and a sufficient condition of robust FTS for uncertain CTLSS. Such sufficient conditions in the LMI formalism are attained for finite-time stability; this gives the opportunity of fitting the finite time stability problem in the general framework of the linear matrix inequality (LMI) approach. In this context an example is provided to demonstrate the application of the proposed method for CTLSS finite-time stability problem.

scholarly journals Exponential Stability of Switched Positive Homogeneous Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Dadong Tian ◽  
Shutang Liu
Keyword(s):  
Nonlinear Systems ◽  
Exponential Stability ◽  
Decay Rate ◽  
Dwell Time ◽  
Vector Fields ◽  
Sufficient Condition ◽  
Time Varying ◽  
Time Switching ◽  
Homogeneous Vector Fields ◽  
Homogeneous Vector

This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-varying delays is derived. In particular, for the corresponding delay-free systems, we prove that this sufficient condition is also necessary. Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.

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