Abstract
In recent years, linear control theories, especially the linear optimal control theories, have come to be developed in a general feedback framework which includes the models of disturbances and plant uncertainties that are are usually known as weighting functions. In such framework, the stability common to both regulator and servomechanism problems requires that the weighted closed loop transfer matrix be stable in addition to the internal stability of the actual feedback system. Since some weighting functions may be unstable, this stability requirement is not always solvable even when the plant is internally stabilizable. Such stability requirement is termed as comprehensive stability and analyzed in this paper. The necessary and sufficient condition is derived in a extremely general case and stated in terms of the invariant-zeros of the given generalized plant which contains the dynamics of the plant and weighting functions. Also, a class of controllers achieving the comprehensive stability is parameterized. This result is believed to form a foundation for a unified control theory of regulator and servomechanism.
