Frequency Stability Analysis of Linear Systems with General Distributed Delays

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

“…It is clear that the matricesX l are non trivial, then the value s 0 belongs to the delay free system (8). This procedure also holds for −s 0 .…”

“…Let s 0 be an eigenvalue of the neutral delay system (1), such that −s 0 is also an eigenvalue of system (1). Then the value s 0 belongs to the spectrum of the delay free system (8).…”

“…This methodology is based on the same concepts as those presented for distributed and point wise delay systems [8]. It exploits the interesting connection between the system spectrum and that of the delay free system used in the computation of the Lyapunov matrix: If s 0 is a root of the delay system such that −s 0 is also a root, then s 0 belongs also to the spectrum of the delay free system.…”

Critical parameters of integral delay systems

“…From the viewpoint adopted in this contribution, a preferable approach has been introduced in and , where the computation of critical parameters of differential delay systems is performed via a delay‐free matrix system of equations, which is derived from the Lyapunov matrix for delay systems. By using some recent results on Lyapunov matrices for time‐delay systems , the approach has been extended to classes of systems with distributed delays and neutral delay systems in and , respectively.…”

Necessary conditions for the exponential stability of time-delay systems via the Lyapunov delay matrix

“…These results have been used to characterize the stability/instability critical values of delay systems, to give sufficient stability conditions by extending the approach of Gu through the proposal of a piecewise linear Lyapunov matrix function , and to provide instability conditions derived from the violation of the lower bound of the functional . They also allowed to characterize and compute the norm of time‐delay systems .…”