Necessary and sufficient stability conditions for integral delay systems

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form 0 1 ( 1) ( ) ( ) x k A x k A x k h + = + − . The time-dependent criteria are derived by Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditi...

Necessary and Sufficient Stability Condition of Discrete State Delay Systems

Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

Necessary and Sufficient Conditions for Delay-dependent Asymptotic Stability of Linear Cotinuous Large Scale Time Delay Autonomous Systems

This paper offers new necessary and sufficient conditions for delaydependent asymptotic stability of the linear continuous large scale time delay systems. The obtained conditions of stability are expressed by nonlinear system of matrix equations and the Lyapunov matrix equation for an ordinary linear continuous system without delay.

Necessary and Sufficient Conditions for Differentiating under the Integral Sign

Necessary and Sufficient Conditions for Stability of LMS

In a recent work [7], some general results on exponential stability of random linear equations are established which can be applied directly to the performance analysis of a wide class of adaptive algorithms, including the basic LMS ones, without requiring stationarity, independency, and boundedness assumptions of the system signals. The current paper attempts to give a complete characterizatio...