Stabilization of time-delay systems through linear differential equations using a descriptor representation

Abstract

Abstract-In this article, a new method to assess stability and to design static state feedback controller for linear timedelay systems is introduced. The method based on linear differential equations allows considering explicit LyapunovKrasovskii functionals with non constant matrix parameters. The stability conditions considering constant delays are delaydependent and expressed using easy computable linear matrix inequalities. An example is introduced to show the efficiency of the stabilization criteria.

Stabilization of uncertain linear distributed delay systems with dissipativity constraints

“…where M ∈ R ρ×ρ and m i (τ ) are linearly independent and that for all i = 1 • • • ρ there exists an uncountable set P ⊆ O such that ∀ϑ ∈ P, m i (ϑ) ̸ = 0. Similar assumptions can be found in [34,19,24,21].…”

“…Since the corresponding delay free system is unstable and distributed term contains a trigonometric function, the methodologies in [27] and [34] are not able to produce any feasible result.…”

On parameterized Lyapunov–Krasovskii functional techniques for investigating singular time-delay systems

“…In this work, a singular-type complete quadratic Lyapunov-Krasovskii functional is introduced in which the parameters are defined using polynomial functions inspired by [14]. A new delay-dependent stability criterion is derived via a linear matrix inequality formulation that can be easily solved by various convex optimization techniques.…”

A design approach for structured controllers for uncertain delay systems grounded in the real structured pseudospectra framework

“…The stabilisation of linear time-delay systems is a topic of major concern in control systems theory and a substantial amount of results have contributed to develop and partially solve this problem; without being exhaustive, possible approaches for stability analysis and stabilization are the use of Lyapunov-Krasovskii functionals and LMI conditions (see for instance [5,25,27]), the direct eigenvalue optimization approach ( [28]), the continuous pole placement method ( [17]) and the use of prediction based controllers (see [14] and references therein, [24,20]). We refer the reader interested in a general overview on the many different stabilisation methods to the monographs [22], [7] and [21].…”