arXiv subjects

Yassine El Gantouh

Publications and source records attributed to Yassine El Gantouh.

8 recordsLinked to original sources

arXiv2026

Exponential stability of abstract boundary-coupled positive systems

In this paper, we study the well-posedness and exponential stability of a class of abstract boundary-coupled positive systems. Within a general semigroup framework, we establish well-posedness in terms of existence, uniqueness, and regularity of solutions. More concretely, we derive some simple and readily verifiable tests on the boundary coupling operators for the verification of the well-posedness of the coupled system and, at the same time, provide spectral criteria that guarantee exponential stability of the solutions. The analysis is based on two complementary approaches: the feedback-theoretic method and perturbation techniques for resolvent positive operators on Banach lattices (i.e., Banach spaces equipped with a compatible order structure). This unified framework allows for a systematic treatment of a broad class of boundary couplings in abstract dynamical systems. Several examples are presented to illustrate the applicability of the theoretical results.

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arXiv2026

A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings

We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a spectral small-gain condition ensuring exponential ISS. We further investigate linear Boltzmann-type equations on an infinite network of intersecting circles, incorporating delays, scattering, and disturbances acting at the junction. For this class of systems, we prove that a spectral small-gain condition on the transmission operator matrix guarantees exponential ISS with respect to disturbances propagating through the network. Moreover, we derive explicit ISS estimates for {certain} classes of dynamical processes. Finally, we demonstrate the practical applicability of our results by considering two important classes of time-delayed transmission conditions.

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arXiv2026

Admissibility of control operators for positive semigroups and robustness of input-to-state stability

In this paper, we investigate well-posedness and stability properties of distributed parameter systems, with particular emphasis on linear positive control systems. We establish a characterization of the well-posedness in the Banach lattice setting. Furthermore, we derive a resolvent condition for admissibility of control operators for positive semigroups. In addition, we study the behavior of input-to-state stability (ISS) under unbounded perturbations of the underlying semigroup generator. More precisely, we establish necessary and sufficient conditions for the robustness of ISS under Desch-Schappacher perturbations. Our theoretical results are demonstrated through a boundary value-controlled transport equation with non-local boundary conditions.

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arXiv2026

Well-posedness of boundary control systems and application to ISS for coupled heat equations with boundary disturbances and delays

This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence of solutions on the initial data and $L^p$-inputs. The proof relies on a new boundedness estimate for the input/output maps of linear time-invariant infinite-dimensional systems with unbounded control and observation operators. The developed technique is applied to derive specific conditions for the exponential input-to-state stability of boundary-coupled heat equations with boundary disturbances and time-delays.

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arXiv2025

Well-posedness and stability of boundary delay equations

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the existence, uniqueness, and positivity of solutions. Furthermore, we derive spectral criteria for exponential stability. The conditions on the perturbation generalize well-known criteria for the generation of domain perturbations of positive semigroup generators. As an application, we present necessary and sufficient conditions for the exponential stability of positive hyperbolic systems with time-delayed boundary conditions.

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arXiv2023

Positivity of infinite-dimensional linear systems

In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of systems. This latter effort is motivated in part by a complete description of well-posed positive control/observation systems. An interesting feature of positive well-posed linear systems is that weak regularity and strong regularity, in the sense of Salamon and Weiss, are equivalent. Moreover, we provide sufficient conditions for zero-class admissibility for positive semigroups. In the context of positive perturbations of positive semigroups, we establish two perturbation results, namely the Desch-Schappacher perturbation and the Staffans-Weiss perturbation. As for illustration, these findings are applied to investigate the existence and uniqueness of a positive mild solution of the linear Boltzmann equation with non-local boundary conditions on finite network.

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arXiv2023

Boundary approximate controllability under positivity constraints of linear systems

This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability result under positivity constraints on the control for such systems. Then, and more importantly, we provide a necessary and sufficient condition for controllability under positivity constraints on the control and the state. The obtained results are applied to the controllability of transportation and heat conduction networks. In particular, provided that the underlying graph is strongly connected, the controllability under positivity constraints on the control/state of transport network systems is fully characterized by a Kalman-type rank condition. For a system of heat equations with Robin boundary conditions on a path-like network, we establish approximate controllability under positivity state-constraint with a single positive input through the starting node. However, we prove the lack of controllability under unilateral control-constraint.

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arXiv2021

Well-posedness and approximate controllability of neutral network systems

In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the rich theory of infinite-dimensional linear systems to derive necessary and sufficient conditions for approximate controllability. Moreover, we propose a rank condition for which we can easily verify the conditions of controllability. Our approach is mainly based on the feedback theory of regular linear systems in the Salamon-Weiss sense.

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