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Accelerating simulation time of unstable discrete-time systems using Singular Perturbation Approximation

In the natural phenomenon, many systems are unstable. Moreover, the systems in the universe often have large order. The system that has a large order is more complicated than the system that has a small order. Therefore, we need to simplify the order of the system without any significant errors. Simplification of the system can be done using the reduction of the model. Model reduction can only be done on the stable system, so that the unstable system needs to be decomposed to obtain a stable subsystem that can be reduced. Singular Perturbation Approximation (SPA) method is one of the model reduction method. The reduced models are obtained by taking the speed of fast mode equal to zero. According to our simulation result using MATLAB, for reduced model having a small order (many state variables are removed) in low frequency, the model reduced using SPA is closer to original model compared with the model reduced using Balanced Truncation (BT). The time needed to simulate the reduced model is smaller than the time needed to simulate the original model. However, when the order of reduced model is small, then the error is big.