The Corduneanu-Popov Approach to the Stability of Nonlinear Time-Varying Systems

1970 ◽  
Vol 18 (2) ◽  
pp. 267-281 ◽  
Author(s):  
James H. Taylor ◽  
Kumpati S. Narendra
Keyword(s):  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

On the Stability of a Certain Class of Linear Time-Varying Systems

2005 ◽  
Vol 2 (8) ◽  
pp. 1240-1245 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

On the Stability of Discrete Time-Varying Systems

2010 ◽  
Author(s):  
A. Czornik ◽  
A. Nawrat
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

On the stability of time-varying systems using an observer for feedback control†

1971 ◽  
Vol 14 (6) ◽  
pp. 1081-1087 ◽  
Author(s):  
BAHAR J. UTTAM
Keyword(s):  
Feedback Control ◽  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

Partial stability analysis of nonlinear time-varying impulsive systems

2019 ◽  
Vol 12 (06) ◽  
pp. 1950066
Author(s):  
Boulbaba Ghanmi
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Time Varying ◽  
Impulsive Systems ◽  
Partial Stability ◽  
Stability Theorems ◽  
Time Varying Systems ◽  
The Stability ◽  
Derivatives Of ◽  
Theoretical Results

This paper investigates the stability analysis with respect to part of the variables of nonlinear time-varying systems with impulse effect. The approach presented is based on the specially introduced piecewise continuous Lyapunov functions. The Lyapunov stability theorems with respect to part of the variables are generalized in the sense that the time derivatives of the Lyapunov functions are allowed to be indefinite. With the help of the notion of stable functions, asymptotic partial stability, exponential partial stability, input-to-state partial stability (ISPS) and integral input-to-state partial stability (iISPS) are considered. Three numerical examples are provided to illustrate the effectiveness of the proposed theoretical results.

On the stability of time-varying systems

1966 ◽  
Vol 11 (4) ◽  
pp. 746-746
Author(s):  
D. Eller ◽  
J. Aggarwal
Keyword(s):  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

scholarly journals A lower bound for the stability radius of time-varying systems

2004 ◽  
Vol 132 (12) ◽  
pp. 3653-3659 ◽  
Author(s):  
Adina Luminiţa Sasu ◽  
Bogdan Sasu
Keyword(s):  
Lower Bound ◽  
Stability Radius ◽  
Time Varying ◽  
Time Varying Systems ◽  
The Stability

scholarly journals Asymptotic Stability of Distributed-Order Nonlinear Time-Varying Systems with the Prabhakar Fractional Derivatives

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
MohammadHossein Derakhshan ◽  
Azim Aminataei
Keyword(s):  
Asymptotic Stability ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Time Varying ◽  
Lyapunov Direct Method ◽  
Fractional Differential Systems ◽  
Time Varying Systems ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

In this article, we survey the Lyapunov direct method for distributed-order nonlinear time-varying systems with the Prabhakar fractional derivatives. We provide various ways to determine the stability or asymptotic stability for these types of fractional differential systems. Some examples are applied to determine the stability of certain distributed-order systems.

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