Related papers: Disturbance-to-state stabilization by output feedb…
In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control.…
In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the…
This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance.…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…
This paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
In this paper, we consider boundary stabilization for a cascade of ODE-heat system with state delay under actuator saturation. To stabilize the system, we design a state feedback controller via the backstepping method and find a bound on…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence of Dirichlet-Robin boundary disturbances, as well as…
This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output…
This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are…
This paper addresses the problem of feedback stabilization of a cascade of two heat equations that are coupled in the boundary conditions, the input being a boundary control for the first component of the cascade. Two distinct control input…
We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay,…
The main aim of this paper is to provide a new feedback law for the heat equations in a bounded domain $\Omega $ with Dirichlet boundary condition. Two constraints will be compulsory: First, The controls are active in a subdomain of $\Omega…
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it…
This is the first part of four series papers, aiming at the problem of actuator dynamics compensation for linear systems. We consider the stabilization of a type of cascade abstract linear systems which model the actuator dynamics…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…