Leith, D. J. and Leithead, W.E.
Gain-Scheduled & Nonlinear Systems: Dynamic Analysis by Velocity-Based Linearisation Families.
International Journal of Control, 70.
A family of velocity-based linearisations is proposed for a nonlinear system. In contrast to the
conventional series expansion linearisation, a member of the family of velocity-based linearisations is
valid in the vicinity of any operating point, not just an equilibrium operating point. The velocity-based
linearisations facilitate dynamic analysis far from the equilibrium operating points and enable the
transient behaviour of the nonlinear system to be investigated. Using velocity-based linearisations,
stability conditions are derived for both smooth and non-smooth nonlinear systems which avoid the
restrictions, to trajectories lying within an unnecessarily, perhaps excessively, small neighbourhood
about the equilibrium operating points, inherent in existing frozen-input theory. For systems where
there is no restriction on the rate of variation, the velocity-based linearisation analysis is global in
nature. The analysis techniques developed, whilst quite general, are motivated by the gain-scheduling
design approach and have the potential for direct application to the analysis of gain-scheduled systems.
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