H∞-Control With State-Feedback For Nonsmooth Pritchard-Salamon Systems

Zames[23] has presented a theory of optimal H&-control in order to improve the robustness of a system.This theory has been extended by Pritchard and Salamon to allow for infinite-dimensional systems in the Pritchard-Salamon class.Then,Doyle et al [5] have proved that the solution of the Hx梒ontrol problem for finite-dimensional linear systems was attained by solving the corresponding Riccati equations.Curtain and Z\vart[3] have solved the H^梒ontrol problem for infinite-dimensional linear systems with bounded input and output operators by the similar way.However, for infinite-dimensional linear systems with unbouned input and output opreators(Pritchard-Salamon systems),the Hoc-control problem has been solved by Keulen[10] under the smooth condition.lt is well known that nonsmooth Pritchard-Salamon systems are existed and significant.Therefore.Curtain et al[2]have presented an open problem as to whether the smooth condition is necessary.At recent.Guo,Zhang and Huang[8] have attained a profound result for the perturbed theory of nonsmooth Pritchard-Salamon systems.Using this result,we consider the Hx梒ontrol problem with state feedback for nonsmooth Pritchard-Salamon systems,and attain the result that the existence of admissible state feedback for a nonsmooth Pritchard-Salamon system is equavlent to the solvability of an operator Riccati equation.So we solve the open problem in part presented by Curtain et al.