Finite-time stability of spring-mass system with unilateral impact constraints and frictions

2020 ◽  
Vol 34 (30) ◽  
pp. 2050341
Author(s):  
Ruiyang Qiu ◽  
Ruihai Li
Keyword(s):  
Finite Time ◽  
Sliding Friction ◽  
Sufficient Conditions ◽  
Step Function ◽  
Time Varying ◽  
Time Stability ◽  
Mass System ◽  
Finite Time Stability ◽  
Air Resistance ◽  
Theoretical Results

In this paper, a spring-mass system with impacts and frictions is formulated by the impulsive differential system. An energy-like Lyapunov function and an auxiliary step function are constructed to analyze the finite-time stability of such impact system with a time-varying external force and sliding friction as well as air resistance. We establish the sufficient conditions of finite-time stability for three cases of the spring-mass system, and present numerical simulations for each case to verify the validity of the theoretical results.

scholarly journals Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3321
Author(s):  
Issaraporn Khonchaiyaphum ◽  
Nayika Samorn ◽  
Thongchai Botmart ◽  
Kanit Mukdasai
Keyword(s):  
Neural Networks ◽  
Integral Inequality ◽  
Finite Time ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Passivity Analysis

This research study investigates the issue of finite-time passivity analysis of neutral-type neural networks with mixed time-varying delays. The time-varying delays are distributed, discrete and neutral in that the upper bounds for the delays are available. We are investigating the creation of sufficient conditions for finite boundness, finite-time stability and finite-time passivity, which has never been performed before. First, we create a new Lyapunov–Krasovskii functional, Peng–Park’s integral inequality, descriptor model transformation and zero equation use, and then we use Wirtinger’s integral inequality technique. New finite-time stability necessary conditions are constructed in terms of linear matrix inequalities in order to guarantee finite-time stability for the system. Finally, numerical examples are presented to demonstrate the result’s effectiveness. Moreover, our proposed criteria are less conservative than prior studies in terms of larger time-delay bounds.

scholarly journals Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo
Keyword(s):  
Finite Time ◽  
Time Varying ◽  
Stability Of Solutions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Difference Systems ◽  
Fractional Delay ◽  
Delay Difference ◽  
New Criteria ◽  
Theoretical Results

This paper focuses on the uniqueness and novel finite-time stability of solutions for a kind of fractional-order nonlinear difference equations with time-varying delays. Under some new criteria and by applying the generalized Gronwall inequality, the new constructive results have been established in the literature. As an application, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.

scholarly journals New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten B. Stojanovic
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature.

scholarly journals Delay-Dependent Finite-Time andL2-Gain Analysis for Switched Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Qiongfen Yang
Keyword(s):  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switching Behavior ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

For the switched systems, switching behavior always affects the finite-time stability (FTS) property, which was neglected by most previous studies. This paper is mainly concerned with the problem of delay-dependent finite-time andL2-gain analysis for switched systems with time-varying delay. Several less conservative sufficient conditions related to finite-time stability and boundness of switched system with time-varying delays are proposed; the system trajectory stays within a special bound with the information of switching signal. At last, a numerical example is also given to illustrate the efficiency of the developed method.

scholarly journals On necessary and sufficient conditions for output finite-time stability

Automatica ◽  
2021 ◽  
Vol 125 ◽  
pp. 109427
Author(s):  
Konstantin Zimenko ◽  
Denis Efimov ◽  
Andrey Polyakov ◽  
Artem Kremlev
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Time Stability ◽  
Finite Time Stability ◽  
Necessary And Sufficient

scholarly journals Finite-TimeH∞Control for Time-Delayed Stochastic Systems with Markovian Switching

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenhua Gao ◽  
Feiqi Deng ◽  
Ruiqiu Zhang ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Time Stability ◽  
Finite Time Stability ◽  
Weighting Matrix ◽  
Simulation Results ◽  
Dependent State

This paper studies the problem of finite-timeH∞control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-timeH∞control is obtained. Simulation results illustrate the effectiveness of the proposed method.

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