Solution of H∞ control problem for hybrid periodic infinite dimensional systems and general quadratic forms. I

We consider the H_∞ control problem for a class of infinite- dimensional systems (so called Pritchard-Salamon systems) with periodic coefficients and arbitrary quadratic functional. All necessary definitions are introduced and exact analoques of classical results are obtained. The paper extends the known solution of the γ-attenuation control problem for C⁰-simigroups to the case of periodic systems and possibly sign-indefinite quadratic functional. The sampled-data (or hybrid) systems are also covered.