Abstract
RH∞-Optimization problem of minimizing cost function ||T-UV||∞ is considered in the case of T and U being given square transfer matrices and V to be found. The result to the problem is already known in the literatures. The present derivation is, however quite elementary. Only simple matrix manipulations and results in linear system theory are used.
The problem is solved in state space, based on the definition of norm ||·||∞. Firstly, with the state space realization of U-1 and U-1T, a lower bound σ of cost ||T-UV||∞ is found. Then it is shown that there exists a Vs∈RH∞, parameterized as Vs=D+sNs with free parameter matrix S, satisfying inequality ||T-UV||∞≤σ, which, therefore, implies that σ is the minimum. Finally, the fact that all V's∈RH∞ minimizing ||T-UV||∞ take the form Vs will be proved.
