Control of a Time Delay System Arising From Linearized Conservation Laws

A structure of energy cogeneration with distributed parameters is considered, modeled by an initial boundary value problem for hyperbolic conservation laws with a nonlinear and nonstandard boundary condition. Under a standard simplifying assumption leading to linear partial differential equations, the model is studied by associating a system of functional differential and difference equations of neutral type: considered are basic theory (existence, uniqueness, and continuous data dependence), invariant sets (positiveness of some state variables), equilibria, and their inherent stability (without control). These properties are illustrated by simulation results. Furthermore, a control Lyapunov functional is constructed, and feedback stabilizing structure is designed. This paper ends with a conclusion section, where open problems, such as stability by the first approximation/robustness and stability preservation under singular perturbations, are pointed out.