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We construct an explicit Lyapunov function for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. We assume the nonlinearity is even in the advection term. We follow a method originally suggested by…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…
In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…
In this work we study a degenerate pseudo-parabolic system with cross diffusion describing the evolution of the densities of an unsaturated two-phase flow mixture with dynamic capillary pressure in porous medium with saturation-dependent…
A delay Lyapunov matrix corresponding to an exponentially stable system of linear time-invariant delay differential equations can be characterized as the solution of a boundary value problem involving a matrix valued delay differential…
This article deals with the design of saturated controls in the context of partial differential equations. It is focused on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces. The aim of…
This paper studies set-invariance and stabilization of hyperbolic sets over rate-limited channels for discrete-time control systems. We first investigate structural and control-theoretic properties of hyperbolic sets, in particular such…
We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
We discuss recent progress in understanding the dynamical properties of partially hyperbolic diffeomorphisms that preserve volume. The main topics addressed are density of stable ergodicity and stable accessibility, center Lyapunov…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…
The behavior of solutions to an initial boundary value problem for a hyperbolic system with relaxation is studied when the relaxation parameter is small, by using the method of Fourier Series and the energy method.
We are concerned with global solutions of multidimensional Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous…