Hanen Damak

1. Singular systems, also referred to in the literature as descriptor systems, differential-algebraic systems, semi-state systems, or generalised state-space systems, are characterised by a mixture...

In this study, the global practical Mittag–Leffler stabilization of a class of nonlinear fractional‐order systems satisfying a (weak) one‐sided Lipschitz condition is investigated. For the considered one‐sided Lipschitz nonlinear systems, a sufficient condition ensuring the existence of a state observer is first established. Then, an observer‐based state feedback controller is proposed, and conditions guaranteeing the practical stability of the resulting closed‐loop fractional‐order system are derived via a linear matrix inequality approach. The separation principle is obtained for the observer‐based control design. The main results extend and improve existing results in the literature. A numerical example is provided to illustrate the effectiveness and applicability of the proposed approach.

This paper investigates the boundedness and practical stability properties of solutions for a class of neural differential equations inspired by Hopfield-type neural networks. Specifically, we develop a novel analytical framework that extends beyond traditional Lyapunov stability theory, Barbalat-type arguments, and fixed-point methods by relaxing common structural assumptions such as smoothness and global Lipschitz continuity. Our approach broadens the class of admissible systems to include nonlinearities with weaker growth conditions and time-varying perturbations that are not easily handled by classical techniques. Sufficient conditions are established to ensure the existence of a globally exponentially stable neighborhood of the origin, even in the presence of varying perturbation conditions. Furthermore, numerical examples are provided to demonstrate and validate the main result.

Practical observers have been extensively investigated in the literature for estimating states in finite-dimensional systems. However, much less attention has been given to their application in infinite-dimensional settings, such as semilinear evolution equations with Lipschitz nonlinearities and unknown inputs. To the best of the authors' knowledge, no previous works have developed a practical observer framework specifically aimed at reconstructing both the system states and sensor faults for this class of systems. In this paper, we propose an unknown input observer design that is applicable to a broad range of semilinear systems. The theoretical results are validated through a numerical simulation, illustrating the efficiency and robustness of the proposed approach.

We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In particular, input-to-state stability of linear time-varying control systems in Hilbert spaces with bounded input operators is discussed. Methods for the construction of non-coercive LISS/iISS Lyapunov functions are presented for a certain class of time-varying semi-linear evolution equations. Two examples are given to illustrate the effectiveness of the results.

In this paper, issues of both attractivity and stability for some classes of nonlinear systems are investigated. New sufficient conditions for practical h-stability of non-autonomous nonlinear systems depending on a parameter are proposed by indefinite Lyapunov functions. We present new converse Lyapunov theorems for non-autonomous systems. The h-stability analysis is achieved with the help of scalar practical h-stable functions. These results are used to study the uniform practical h-stability of non-autonomous perturbed systems.

The purpose of this paper is to introduce a comprehensive approach to designing a robust observer for bilinear evolution equations in Hilbert spaces. This approach is aimed at effectively handling external disturbances while improving system performance and stability. The paper focuses on developing innovative tools and methods to accurately estimate the system state even under the influence of external factors. These contributions are intended to enhance the broader field of control theory and dynamical systems applications. Overall, the research presented in this paper aims to improve our understanding of robust observer design for bilinear evolution equations and its practical applications.