POLYNOMIAL APPROACH TO H-INFINITY CONTROL PROBLEM WITH ADDITIONAL CONSTRAINTS

The H-infinity control problem for linear stationary systems was studi ed in detail in a great number of articles beginning from the work by G. Zames [1]. Nowadays different approaches to its solution were propo sed. They include spectral methods [2], state-space solution [3], poly nomial approaches [4, 5]. All these methods are based on the main proc edure which solves one the following equivalent problems: Nehari probl em in the spectral method, J-spectral factorization in polynomial appr oaches and Riccati equation for the state-space solution. We show in t his article that only standard spectral factorization is needed for to solve the standard problem of minimization of nonnegative cost functi on in the case of full information. The polynomial approach proposed b elow is based on a polynomial analogue of the Riccati equation. This a pproach allows one to fulfil all operations with initial polynomial ma trices only, without their preliminary transformations into state-spac e form or different factorizations. The problem is solved also for the general case in which the quadratic form in the cost function is not assumed to be nonnegative. In the first part of this paper the conditi onal problem of H-infinity-minimization is considered. It is reduced t o H-infinity control problems with parameters but without additional r estrictions. The method of this reduction is based on so-called S-proc edure which was previously used in the absolute stability theory [6].