Pole-zero cancellation and state/output equations

State-space modeling of linear time-invariant RLC circuits with independent sources is discussed. The principle idea presented is two-fold. In the first part it is shown that, if the circuit considered has capacitor and current source-only cut sets, and/or inductor and voltage source-only loops, then a new set of state equations can be obtained which will have lower dimension compared to the state equations obtained using the standard textbook approach. In the second part it demonstrated that further reductions are possible if the state equations are written at other coordinate systems rather than the usual Cartesian coordinates