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 )
Old post..
Once you have derived the state-space representation of your electrical circuit, you can use any suitable ODE solver to run the time-domain simulation.
The harder part is the derivation of the state-space equations from a netlist via MNA or a tree approach.
See ANALOG CIRCUIT SIMULATION BY STATE VARIABLE METHOD by Rodica VOICULESCU1 and Mihai IORDACHE
Commercial simulators along these lines are PLECS, PSIM, Simplis, SimPowerSystems etc.
The classic book 'Computer-aided Analysis of Electronic Circuits: Algorithms and Computational Techniques' by Leon O. Chua and Pen-Min Lin contains a description of state-space based simulators. I found the book sufficiently detailed to successfully write a simulator for piece-wise linear networks with ideal switches.
When you are primarily interested in non-linear networks (semiconductors, nonlinear inductors and capacitors, etc.) an MNA-based SPICE-like approach is probably a much better idea. The book also contains these basic algorithms (in unparalleled depth), but has nothing on device modeling.
