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

Robustness of Time-Varying Systems

1997 ◽  
Author(s):  
Fritz Colonius ◽  
Wolfgang Kliemann
Keyword(s):  
Equilibrium Point ◽  
Vector Fields ◽  
Dimensional Space ◽  
Stability Radius ◽  
Time Varying ◽  
Modeling Uncertainties ◽  
Time Varying Systems ◽  
The Stability ◽  
The One ◽  
Stability Radii

Abstract The dynamics of many mechanical systems can be described, or approximated by smooth vector fields in d-dimensional space Rd. External and internal excitations as well as modeling uncertainties are incorporated in the vector fields as families of (time-varying) functions, possibly with their own dynamics. The problem then is to study the response behavior of the system under the given uncertainty structure. In this paper we analyze the stability of uncertain systems at an equilibrium point, using the concept of stability radii. Roughly, a stability radius is the smallest excitation range such that a (time-varying) perturbation within this range can render the system unstable. Since we consider time-varying perturbations, the precise stability radius of the system is determined by the maximal Lyapunov exponent of the linearization at the equilibrium point. Several examples illustrate the theory and compare the precise stability radius to the one obtained via Lyapunov function techniques.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document