Realization, design and implementation of row-pseudoproper left matrix fraction descriptions with impulsive modes

Abstract

A novel and minimal realization algorithm is proposed for determining generalized state-space representation from a so-called row-pseudoproper left matrix fraction description (LMFD). The realized system with the state-space representation form is proved to be controllable and observable in the sense of [1,2] if the given row-pseudoproper MFD is left coprime. Besides, the proposed state feedback control law not only satisfies the optimal regional-pole-placement design for the realized generalized dynamical system, but also eliminates the impulsive terms in the state response of the closed-loop system. For practical consideration, an equivalent input-output feedback structure of the designed state-feedback controller is adopted. Based on the cascaded and/or parallel active RC networks with better sensitivity and stability properties, the resulting structure of the equivalent input-output feedback controller can be readily implemented based on proper subsystems.