As far as I know there is no state-space based general purpose circuit simulator around. Though there are certain algorithm to figure out how to find state-spaces (unique?) in a circuit (represented by graphs). Has anyone tried writing a program to simulate some basic circuit elements?
[ref] 1. Sheshu and Reed, Electrical networks and graph theory. [ref] 2. H Narayanan, Submodular Functions and Electrical Networks ( http://www.ee.iitb.ac.in/~hn )