Balanced structures and model reduction of unstable systems

It is shown that B.C. Moore's balancing model (1981) can be extended to unstable systems by utilizing two weighted Grammian matrices. It is proposed that the J omega axis can be shifted to handle unstable systems. The balanced approach involves the solution of two modified Lyapunov equations. Two numerical examples are given to illustrate the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>