Non-smooth Of H_ ¡Þ - Pritchard,-salamon System With Observation Feedback Control

For a realistic control system perturbed by all kinds of factors exterior or interior, we always expect to design a controller which not only can stabilize the system itself, but also stabilize the system when some kinds of perturbation disturbed it,so as to minimize the influence of the system. When the optimum measured by the norm of corresponding transfer function in frequency domain, this kind of design of optional controller is called H∞-Control. Much work have been done on H∞-Control. For the finite-dimensional linear system, Doyle[l]and Kimura[2] had proved the results that the solution of H∞-Control can be obtained by solving two algebraic Riccati equations. The same as the infinite-dimensional linear system with bounded input and output operators in R.F.Curtain[3]. Many control problems described by linear partial differential equations regarding boundary control and boundary observation are put forward in engineering science, and boundary control and boundary observation lead to the research of the H∞-control theory of infinite-dimensional systems with unbounded inputs and outputs. This kind of problems can be described by the state-space of Co-semigroup in Hilbert space. One of the important classes is Pritchard-Salamon system with unbounded admissible input operator and output operator. Keulen[4]and Curtain[5] has finished excellent work, but they added smooth condition when they transform the solution of "H∞-Control into solving two algebraic Riccati equations. Recently, some work is expanded about nonsmooth Pritchard-Salamon system. Based on the results, we proved that solution of "H∞-Control is equivalent to solving two algebraic Riccati equations. So,we partly answered the open problem brought forward by Curtain[5],that is whether the domain condition D(AV) C W is necessary in the constructive argument.