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Hybrid passivity and finite gain stability theorem: stability and control of systems possessing passivity violations

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2 Author(s)
Forbes, J.R. ; Inst. for Aerosp. Studies, Univ. of Toronto, Toronto, ON, Canada ; Damaren, C.J.

The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal low-pass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input-output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.

Published in:

Control Theory & Applications, IET  (Volume:4 ,  Issue: 9 )