An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is
presented. The main results and proofs are presented in details for the case of systems with …

It is widely known that the solutions of Lyapunov equations can be used to compute the H 2
norm of linear time-invariant (LTI) dynamical systems. In this paper, we show how this theory …

We present necessary conditions for the exponential stability of linear systems with multiple
delays. They are expressed in terms of the delay Lyapunov matrix of the Lyapunov …

We propose a novel approach for the optimization of the H 2 norm for time-delay systems,
grounded in its characterization in terms of the delay Lyapunov matrix. We show how the …

The maximum of the norm of the delay Lyapunov matrix function of exponentially stable
linear time-delay systems is proven to be achieved at zero. We apply this result to the robust …

Balanced truncation is a standard and very natural approach to approximate dynamical
systems. We present a version of balanced truncation for model order reduction of linear …

This paper presents a criterion of exponential stability for time-invariant linear delay systems
of retarded type. The criterion, which is based on the delay Lyapunov matrix, generalizes the …

The paper deals with the computation of delay Lyapunov matrices for linear exponentially
stable time-invariant systems with several pointwise delays. It is shown that the matrices …

The Lyapunov matrix is a key element of the construction of Lyapunov–Krasovskii
functionals with prescribed derivative for linear time-invariant time delay systems. Moreover …

Exponential necessary stability conditions for linear systems with multiple delays are
presented. The originality of these conditions is that, in analogy with the case of delay free …