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Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
We consider an interlinked production model consisting of conservation laws (PDE) coupled to ordinary differential equations (ODE). Our focus is the analysis of control laws for the coupled system and corresponding stabilization questions…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions…
This paper is concerned with the stability analysis of encrypted observer-based control for linear continuous-time systems. Since conventional encryption has limited ability to deploy in continuous-time integral computation, our work…
This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus $\mathbb{T}^{2}.$ The control function is considered to be acting on a small vertical…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
In this paper, we consider a dissipative system of one-dimensional piezoelectric beam with magnetic effect and a tip load at the free end of the beam, which is modeled as a special form of double boundary dissipation. Our main aim is to…
Recent advances in learning-based control leverage deep function approximators, such as neural networks, to model the evolution of controlled dynamical systems over time. However, the problem of learning a dynamics model and a stabilizing…
This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
We address the problem of stability of synchronization in two diffu- sively coupled oscillators under small perturations. We have two cases, namely, when the perturation becomes of a linear operator and the case of non-linear operator. We…
Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
We study the control of networked systems with the goal of optimizing both transient and steady-state performances while providing stability guarantees. Linear proportional-integral (PI) controllers are almost always used in practice, but…
This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…