Multi-time-scale systems control via use of combined controllers

We propose a method based on the Schur decomposition that simplifies the study of multiple-time-scale singularly perturbed systems while retaining time-scale properties. The transformed system is sequentially decoupled using the Chang transformation to separate it into individual time-scales. Furthermore, control strategies have been applied to the Schur-transformed system. Initially, controller design based on the eigenvalue placement is proposed where state vectors of each time-scale are used for feedback. Then, a combined eigenvalue placement-linear quadratic controller scheme is studied. The combined design strategy offers flexibility and can be more effective for specific control problems.

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