New sufficient conditions for the stability of slowly varying linear systems

1993 ◽  
Vol 38 (9) ◽  
pp. 1409-1411 ◽  
Author(s):  
F. Amato ◽  
G. Celentano ◽  
F. Garofalo
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
The Stability

Stability and controllability of switched systems

2013 ◽  
Vol 61 (3) ◽  
pp. 547-555 ◽  
Author(s):  
J. Klamka ◽  
A. Czornik ◽  
M. Niezabitowski
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Systems ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Arbitrary Switching ◽  
Mathematical Problems ◽  
The Stability ◽  
Necessary And Sufficient

Abstract The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results.

scholarly journals Common Weak Linear Copositive Lyapunov Functions for Positive Switched Linear Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuangong Sun ◽  
Zhaorong Wu ◽  
Fanwei Meng
Keyword(s):  
Stability Analysis ◽  
Complex Systems ◽  
Linear Systems ◽  
Algebraic Structure ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Switched Linear Systems ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov functions play a key role in the stability analysis of complex systems. In this paper, we study the existence of a class of common weak linear copositive Lyapunov functions (CWCLFs) for positive switched linear systems (PSLSs) which generalize the conventional common linear copositive Lyapunov functions (CLCLFs) and can be used as handy tool to deal with the stability of PSLSs not covered by CLCLFs. We not only establish necessary and sufficient conditions for the existence of CWCLFs but also clearly describe the algebraic structure of all CWCLFs. Numerical examples are also given to demonstrate the effectiveness of the obtained 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 New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

scholarly journals The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 353 ◽  
Author(s):  
Hanaa Zitane ◽  
Ali Boutoulout ◽  
Delfim F. M. Torres
Keyword(s):  
Linear Systems ◽  
Sufficient Conditions ◽  
Strong Stability ◽  
Decomposition Approach ◽  
Strongly Continuous Semigroups ◽  
Infinite Dimensional ◽  
Strong Stabilization ◽  
Fractional Differential ◽  
Stability And Stabilization ◽  
The Stability

We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics are symmetric and uniformly elliptical and by using the properties of the Mittag–Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.

Stability criteria for linear systems and realizability criteria for RC networks

1957 ◽  
Vol 53 (4) ◽  
pp. 878-896 ◽  
Author(s):  
A. T. Fuller
Keyword(s):  
Linear Systems ◽  
Characteristic Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Polynomial Equations ◽  
Stability Criteria ◽  
Polynomial Coefficients ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Rc Networks

ABSTRACTA new set of stability criteria for linear systems is derived. This shows that about half of the Hurwitz criteria are redundant when certain of the coefficients of the characteristic equation are known to be positive. The theory is applied to obtain a very short derivation of the known aperiodicity criteria. The conditions for realizability of RC networks are shown to be closely related to the stability and aperiodicity criteria, and are stated as sets of criteria in terms of the polynomial coefficients. Two basic theorems are involved which give the necessary and sufficient conditions for the roots of two polynomial equations to be real and separated.

scholarly journals Asymptotic stability of positive fractional 2D linear systems

2009 ◽  
Vol 57 (3) ◽  
pp. 289-292 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
2D Systems ◽  
The Stability ◽  
Necessary And Sufficient

Asymptotic stability of positive fractional 2D linear systemsNew necessary and sufficient conditions for the asymptotic stability of the positive fractional 2D systems are established. It is shown that the checking of the asymptotic stability of positive fractional 2D linear systems can be reduced to testing the stability of corresponding 1D positive linear systems.

Limit Cycles Induced by Threshold Nonlinearity in Planar Piecewise Linear Systems of Node-Focus or Node-Center Type

2020 ◽  
Vol 30 (11) ◽  
pp. 2050160
Author(s):  
Jiafu Wang ◽  
Su He ◽  
Lihong Huang
Keyword(s):  
Linear Systems ◽  
Limit Cycles ◽  
Piecewise Linear ◽  
Sufficient Conditions ◽  
Displacement Function ◽  
Differential Systems ◽  
Exact Number ◽  
Minimum Number ◽  
Focus Type ◽  
The Stability

In this paper, we investigate limit cycles induced by threshold nonlinearity of piecewise linear (PWL) differential systems, which are node-focus type or node-center type with the focus or the center being virtual or boundary. To get the number and stability of limit cycles, we adopt a new displacement function with a better configuration than usual. For a given parameter subregion, we exhibit the exact number or the minimum number of limit cycles. In particular, sufficient conditions are established ensuring that there are exactly two limit cycles. When the focus is boundary, we not only show that the maximum number is two, but also verify that the exact number is zero, one or two by varying parameter subregions. Finally, the exact number as well as the stability are obtained in different parameter regions for the PWL differential systems of node-center type.

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