Incremental quadratic stability

By Luis D'Alto, Martin J. Corless. 2013

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The concept of incremental quadratic stability ($\delta$QS) is very useful in treating systems with persistently acting inputs. To illustrate, if a time-invariant $\delta$QS system is subject to a constant input or $T$-periodic input then, all its trajectories exponentially converge to a unique constant or $T$-periodic trajectory, respectively. By considering the relationship of $\delta$QS to the usual concept of quadratic stability, we obtain a useful necessary and sufficient condition for $\delta$QS. A main contribution of the paper is to consider nonlinear/uncertain systems whose state dependent nonlinear/uncertain terms satisfy an incremental quadratic constraint which is characterized by a bunch of symmetric matrices we call incremental multiplier matrices . We obtain linear matrix inequalities whose feasibility guarantee $\delta$QS of these systems. Frequency domain characterizations of $\delta$QS are then obtained from these conditions. By characterizing incremental multiplier matrices for many common classes of nonlinearities, we demonstrate the usefulness of our results.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bd4e61bc436d09d43704526570dde9d63c94e89c

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