It is an important problem whether or not we can reject the disturbances from distributed parameter circuit. In order to analyze this problem structurally, it is necessary to investigate the basic equation of distributed parameter circuit in the framework of state space. Since the basic equation has two parameters for time and space, the state value belongs to an infinite-dimensional space. In this paper, the disturbance-rejection problems with incomplete state feedback and/or incomplete state feedback and feedforward for infinite-dimensional systems are studied in the framework of geometric approach. And under certain assumptions, necessary and/or sufficient conditions for these problems to be solvable are proved.

The disturbance-rejection problem is to find a feedback control law for linear control systems such that the influence of disturbances is completely rejected from the output. In 1970 Wonham and Morse first studied this problem in the framework of the so-called geometric approach. On the other hand, in 1985 Ghosh studied parameter insensitive disturbance-rejection problems with state feedback and with dynamic compensator. In this paper we study the parameter insensitive disturbance-rejection problem with static incomplete-state feedback for linear multivariable systems in the framework of the geometric approach from the mathematical point of view. Necessary conditions and/or sufficient conditions for this problem to be solvable are presented. Finally an illustrative example is presented.