Distributed Systems: Stabilization, Robustness and Optimal Control

Though linear models are frequently used to approximate real dynamical processes for convenience, there are many other real problems that can not be modeled by linear systems, but have bilinear structures. Bilinear systems constitute an intermediate subclass between linear and nonlinear systems. This monograph develops the problem of stabilization and partial stabilization for linear and bilinear distributed systems using suitable control laws among available options. If this is indeed possible, then one usually desires to achieve this steering while optimizing a certain criterion. The proposed stabilizing controls include constrained control laws and provide an explicit decay rate of the stabilized state. The central tool here is the use of feedback in order to correct for deviations from the desired behavior. In this context, the notion of robustness is needed. The mathematical models of our interest are described by distributed linear and bilinear systems, and the applications include parabolic and hyperbolic equations.