Stability and physical realizability considerations in the synthesis of multipole control systems

With the use of the canonical form for a multipole control system as the starting point, the characteristic equation of the system is derived and its roots related to the poles and zeros of the given plant. Conditions are established which must be imposed on the plant to permit the design of a stable system having an arbitrary response. This is followed by the development of a technique which, by imposing constraints on the over-all response, enables the system designer to achieve a stable design even when certain of the plant's poles and zeros lie in an unstable region of the complex frequency plane. The method permits the direct stability design of multipole control systems in a manner similar to that presently possible for the conventional 2-pole systems. It is applicable to continuous-data systems as well as to sampled-data systems.