Gilberto Ochoa

Instability conditions for linear time delay systems: a Lyapunov matrix function approach

Instability conditions for linear time delay systems of retarded type, with distributed delay, and of neutral type are given. The approach is based on using the converse results on the existence of special quadratics lower bounds for the Lyapunov–Krasovskii functional of complete type associated to these systems.

Critical frequencies and parameters for linear delay systems: A Lyapunov matrix approach

Abstract A new method, based on recent results concerning the construction of the Lyapunov matrix of delay systems, reveals conditions under which the characteristic function has a root s 0 such that − s 0 is also a root. As the pure imaginary roots, which are crucial in the stability analysis of time delay systems, are of that type, this method gives rise to a novel approach for the delay independent and delay dependent stability analyses of systems with delay that are multiple of a basic delay, distributed delays and of a class of neutral type time delay systems. A number of examples are given to illustrate the approach and to show its strength.

Time delay systems with distributed delays: Critical values

Abstract In this paper a procedure for the computation of Lyapunov matrix of a time delay systems with a distributed delay is presented. This algorithm consist in solving a two points boundary value problem for a delay free system. Based on this approach a methodology that reveals conditions under which the characteristic function of the delay system has a root s 0 such that — s 0 is also a root of the characteristic function of the delay free system is also given.

Computation of Imaginary Axis Eigenvalues and Critical Parameters for Neutral Time Delay Systems

In this paper, a procedure for the computation of the Lyapunov matrix of neutral type systems, with delays multiple of a basic one, is recalled: It consists in solving a boundary value problem for a delay free system of matrix equations. The important property that the elements of the spectrum of the delay system that are symmetric with respect to the imaginary axis belong to the spectrum of the delay free system is also established. This property is exploited for the determination of the critical values of the time delay system.

Computation of critical parameters for neutral type time delay systems

Abstract In this paper, a procedure for the computation of the Lyapunov matrix of neutral type systems, with delays multiple of a basic one, is recalled: It consists in solving a boundary value problem for a delay free system of matrix equations. The important property that the elements of the spectrum of the delay system that are symmetric with respect to the imaginary axis belong to the spectrum of the delay free system is also established. This property is exploited for the determination of the critical values of the time delay system.

Critical parameters of integral systems with a class of analytic kernels

Abstract The critical frequencies of integral delay systems with a class of analytic kernels are determined via an auxiliary delay free system, and an upper bound on the number of critical frequencies is obtained. The critical delays are obtained by substituting these frequencies into the characteristic equation of the system. The procedure is validated with a number of nontrivial examples.

Instability conditions for neutral type time delay systems

A complete type Lyapunov-Krasovskii functional for neutral type-time delay systems with given cross terms in the time derivative is presented. The facts that the existance of this functional is guaranteed for exponentially stable systems and that it admits a quadratic lower bound allows to propose new instability conditions for this class of systems.

Necessary exponential stability conditions for scalar periodic time-delay systems

In this paper necessary conditions for exponential stability for scalar periodic systems with one delay are presented. They are obtained in the framework of Lyapunov-Krasovskii functionals of complete type and depends exclusively on the Lyapunov delay function of the delay system.