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Remarks on Dwell Time Solutions and Stability of Families of Nonlinear Vector Fields

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2 Author(s)
Bacciotti, A. ; Dept. of Math., Politec. di Torino, Torino, Italy ; Mazzi, L.

In this note, we discuss the problem of stability of (finite or infinite) families of continuous vector fields, all of them asymptotically stable but, in general, not exponentially stable. Under a multiple Liapunov function condition and an average dwell time constraint, we prove that the system possesses a form of stability, weaker than the standard one. The advantage of our results is that the conditions imposed on the Liapunov functions can be verified a priori, with no previous knowledge of the integral curves of the family.

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Automatic Control, IEEE Transactions on  (Volume:54 ,  Issue: 8 )