A necessary and sufficient condition for robust asymptotic stability of time-variant discrete systems

1993 ◽  
Vol 38 (9) ◽  
pp. 1427-1430 ◽  
Author(s):  
P.H. Bauer ◽  
K. Premaratne ◽  
J. Duran
Keyword(s):  
Asymptotic Stability ◽  
Discrete Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Robust Asymptotic Stability

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

1976 ◽  
Vol 74 ◽  
pp. 71-79
Author(s):  
R. Datko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

scholarly journals Lyapunov-Krasovskii stability analysis of nonlinear integro-differential equation

2018 ◽  
Vol 7 (2) ◽  
pp. 53
Author(s):  
Prebo Jackreece
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Integro Differential Equation ◽  
Necessary And Sufficient

The purpose of this paper is to develop a qualitative stability analysis of a class of nonlinear integro-differential equation within the framework of Lyapunov-Krasovskii. We show that the existence of a Lyapunov-Krasovskii functional is a necessary and sufficient condition for the uniform asymptotic stability of the nonlinear Volterra integro-differential equations.

scholarly journals Existence of Ψ-bounded solutions for sylvester matrix dynamical systems on time scales

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4209-4219 ◽  
Author(s):  
Appa Rao ◽  
K.A.S.N.V. Prasad
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Bounded Solution ◽  
Discrete Systems ◽  
Sufficient Condition ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Sylvester Matrix ◽  
Necessary And Sufficient ◽  
Existence Criteria

In this paper, we study the existence criteria for ?-bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of atleast one ?-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue ?-deltaintegrable function F, on time scale T+. Further, we obtain a result relating to asymptotic behavior of ?-bounded solutions of this equation. The results are illustrated with suitable examples.

A Simple Alternative to the Routh-Hurwitz Criterion for Symmetric Systems

1970 ◽  
Vol 37 (4) ◽  
pp. 1168-1170 ◽  
Author(s):  
T. J. Moran
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Necessary And Sufficient Condition ◽  
Principal Coordinates ◽  
Simple Alternative ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Gyroscopic Systems ◽  
Symmetric Systems

A necessary and sufficient condition for the asymptotic stability of damped, linear, symmetric, multidegree of freedon systems is given. The condition is easily applied if the principal coordinates for the undamped system are known. The stability properties of such systems which are not asymptotically stable are investigated and the result is extended to gyroscopic systems.

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