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Robust State-Dependent Switching of Linear Systems With Dwell Time

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2 Author(s)
Allerhand, L.I. ; Sch. of Electr. Eng., Tel Aviv Univ., Tel-Aviv, Israel ; Shaked, U.

A state-dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed. Sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each subsystem such that it is non-increasing at the switching instants. During the dwell time, this function varies piecewise linearly in time. After the dwell, the system switches if the switching results in a decrease in the value of the LF. The method proposed is also applicable to robust stabilization via state-feedback. It is further extended to guarantee a bound on the L2-gain of the switching system; it is also used in deriving state-feedback control law that robustly achieves a prescribed L2 -gain bound.

Published in:

Automatic Control, IEEE Transactions on  (Volume:58 ,  Issue: 4 )