On the stability of slowly time-varying linear systems

1994 ◽  
Vol 7 (4) ◽  
pp. 331-350 ◽  
Author(s):  
Victor Solo
Keyword(s):  
Linear Systems ◽  
Time Varying ◽  
The Stability

scholarly journals New Stability Analysis for Linear Systems with Time-Varying Delay Based on Combined Convex Technique

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Bin Yang ◽  
Chen-xin Fan
Keyword(s):  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Integral Term ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

A novel combined convex method is developed for the stability of linear systems with a time-varying delay. A new delay-dependent stability condition expressed in terms of linear matrix inequalities (LMIs) is derived by employing a dedicated constructed Lyapunov-Krasovskii functional (LKF), utilizing the Wirtinger inequality and the reciprocally convex approach to handle the integral term of quadratic quantities. Different from the previous convex techniques which only tackle the time-varying delay, our method adopts the idea of combined convex technique which can tackle not only the delay but also the delay variation. Four well-known examples are illustrated to show the effectiveness of the proposed results.

On the Stability of Second Order Time Varying Linear Systems

2005 ◽  
Vol 128 (3) ◽  
pp. 408-410 ◽  
Author(s):  
M. Tadi
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Stiffness Matrix ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Second Order ◽  
Time Varying ◽  
The Stability ◽  
Second Order Systems

This note considers the stability of linear time varying second order systems. It studies the case where the stiffness matrix is a function of time. It provides sufficient conditions for stability and asymptotic stability of the system provided that certain conditions on the stiffness matrix are satisfied.

scholarly journals Global Stability of Polytopic Linear Time-Varying Dynamic Systems under Time-Varying Point Delays and Impulsive Controls

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
M. de la Sen
Keyword(s):  
Dynamic System ◽  
Linear Systems ◽  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying ◽  
Linear Time Invariant ◽  
Impulsive Controls ◽  
The Stability ◽  
Time Invariant ◽  
Point Delays

This paper investigates the stability properties of a class of dynamic linear systems possessing several linear time-invariant parameterizations (or configurations) which conform a linear time-varying polytopic dynamic system with a finite number of time-varying time-differentiable point delays. The parameterizations may be timevarying and with bounded discontinuities and they can be subject to mixed regular plus impulsive controls within a sequence of time instants of zero measure. The polytopic parameterization for the dynamics associated with each delay is specific, so that(q+1)polytopic parameterizations are considered for a system withqdelays being also subject to delay-free dynamics. The considered general dynamic system includes, as particular cases, a wide class of switched linear systems whose individual parameterizations are timeinvariant which are governed by a switching rule. However, the dynamic system under consideration is viewed as much more general since it is time-varying with timevarying delays and the bounded discontinuous changes of active parameterizations are generated by impulsive controls in the dynamics and, at the same time, there is not a prescribed set of candidate potential parameterizations.

scholarly journals Stability Analysis of Linear Systems under Time-Varying Samplings by a Non-Standard Discretization Method

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 278 ◽  
Author(s):  
Xiefu Jiang ◽  
Zongming Yin ◽  
Jinjing Wu
Keyword(s):  
Linear Systems ◽  
Stability Criterion ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Time Varying ◽  
Discretization Method ◽  
Sampled Data ◽  
Discrete Time System ◽  
Parameter Uncertainties ◽  
The Stability

This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.

scholarly journals Stability of non-linear systems with time-varying delays

1980 ◽  
Vol 21 (4) ◽  
pp. 452-463
Author(s):  
R. M. Lewis
Keyword(s):  
Linear Systems ◽  
Time Delays ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability

AbstractA condition guranteeing the stability of linear systems with time delays in the interactions among elements is generalized to cover non-linear systems and discontinuous, unbounded delays.

scholarly journals Advanced controller design for uncertain linear systems with time-varying delays via augmented zero equality approach

2021 ◽  
Author(s):  
YongGwon Lee ◽  
Youngjae Kim ◽  
Seungho Kim ◽  
Seunghoon Lee ◽  
Myeongjin Park ◽  
...  
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Time Derivative ◽  
Linear Matrix ◽  
Feasible Region ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Controller Gain ◽  
The Stability ◽  
Uncertain Linear Systems

This paper deals with the stability analysis and controller design for linear systems with time-varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov-Krasovskii functionals, a set of Linear Matrix inequalities is derived to get advanced feasible region of stability, and controller gain matrices which guarantee the asymptotic stability of the concerned systems within maximum bound of time-delays and its time-derivative. To further reduce the conservatism of stabilization criterion a recently developed mathematical technique which constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

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