Minimum dimensional state-space formulation of linear systems

Abstract

The state-space modelling of linear time-invariant RLC circuits with independent sources is reconsidered. The principal idea presented is two-fold. In the first part of the paper it is shown that, if the circuits considered have capacitor and current source-only cut sets and/or inductor and voltage source-only loops, a new set of state equations can be obtained which will have a lower dimension compared with the state equations obtained using the standard textbook approach. A simple algorithm is presented to derive the reduced-order state equations and initial conditions. In the second part of the paper, it is demonstrated that further reductions are possible if the state equations are written at other coordinate systems rather than the usual Cartesian co-ordinates.