Computing frequency response gain for a class of controlled spatio-temporal systems

A bisection algorithm is developed for computing the frequency response gain of a class of controlled spatio- temporal systems, where the plant is a linear time-invariant spatio-temporal system on a one-dimensional compact spatial domain, and the feedback controller is a linear time-invariant temporal system. The problem is formulated as a worst case analysis problem for a new class of finite-horizon systems having switched dynamics. The validity of the proposed method is demonstrated by numerical examples.