## Switching LPV control designs using multiple parameter-dependent Lyapunov functions.(English)Zbl 1133.93370

Summary: We study the switching control of linear parameter-varying (LPV) systems using multiple parameter-dependent Lyapunov functions to improve performance and enhance control design flexibility. A family of LPV controllers is designed, each suitable for a specific parameter subregion. They are switched so that the closed-loop system remains stable and its performance is optimized. Two switching logics, hysteresis switching and switching with average dwell time, are examined. The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions. The hysteresis switching LPV control scheme is then applied to an active magnetic bearing problem.

### MSC:

 93D30 Lyapunov and storage functions 15A39 Linear inequalities of matrices

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### References:

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