相关论文: Boundary stabilization in finite time of one-dimen…

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…

This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…

This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…

This paper presents a boundary control scheme for prescribed-time (PT) stable of flexible string systems via backstepping method, and the dynamics of such systems modeled by Hamilton's principle is described as second-order hyperbolic…

We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…

Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform…

This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra…

This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation…

We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''. In the paper titled ``Backstepping control of a class of…

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…

The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. The main technical point is to show that we…

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is…

This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…

This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…

This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…

For the quite extensively developed PDE backstepping methodology for coupled linear hyperbolic PDEs, we provide a generalization from finite collections of such PDEs, whose states at each location in space are vector-valued, to previously…

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and m leftward convecting transport PDEs. Using the backstepping approach yields solutions to…