A robust control scheme for a class of quasi-linear propagation processes

In this paper the trajectory tracking control problem for a certain class of propagation processes modeled as Quasi-Linear Parameter Varying systems is considered. The propagation physical models are generally described by means of PDEs (partial differential equations). However in real world control problems the PDE models are usually converted into ODEs (ordinary differential equations) models adopting numerical and/or physical approximations. In many practical problems it happens that the propagation dynamics are linear, while the boundary conditions are described by nonlinear algebraic equations. An ad hoc nonlinear trajectory following control scheme is proposed for this class of systems together with a robust performance analysis based on the concept of quadratic stability with an H_∞ norm bound. An LMI based observer synthesis procedure and some heuristics are also proposed to increase the closed loop system performance.