A new balanced realization and model reduction method for unstable systems

Balanced Reduction of Linear Periodic Systems

“…When the period CJ is equal to one (the time-invariant case), the introduced bound for the infinity norm of the model error reduces to the one of time-invariant systems. For time-invariant systems with no poles on the imaginary axis the balanced reduction has been solved also for unstable systems [21], The possible extension of this result also to the class of discrete-time periodic systems is under investigation. …”

Continuous-Time Identification Using LQG-Balanced Model Reduction

“…When A is unstable there is no solution to the Lyapunov equations. Salomon et al (1999) showed that for (A, B) stabilizable, (A, C) detectable there are still relevant solutions obtained by replacing Lyapunov equations with the Riccati equations…”

“…As balanced model reduction only can be applied to stable models, there is a limited applica-tion range for this method. However, Fuhrmann and Ober (1999) and more recently Salomon et al (1999) have suggested a modified balanced model that exploited a modified balancing approach. Instead of solving for a pair of Gramians using Lyapunov function, it was suggested to be replaced by Riccati equation.…”