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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…
This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy…
This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be…
For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator…
We study the stability of the equilibrium points of a skew product system. We analyze the possibility to construct a Lyapunov function using a set of conserved quantities and solving an algebraic system. We apply the theoretical results to…
Studied in this article is non-Markovian open quantum systems parametrized by Hamiltonian H, coupling operator L, and memory kernel function {\gamma}, which is a proper candidate for describing the dynamics of various solid-state quantum…
We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency…
In this paper, we discuss our recent works on the null-controllability, the exact controllability, and the stabilization of linear hyperbolic systems in one dimensional space using boundary controls on one side for the optimal time. Under…
This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…
Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback…
This note is concerned with the stability and stabilization of the linearized spacecraft attitude control system. Necessary and sufficient conditions are respectively provided to guarantee that the considered systems are polynomially stable…