Brief New results for analysis of systems with repeated nonlinearities

Authors:
F. J. D'Amato;M. A. Rotea;A. V. Megretski;U. T. JöNsson
Affiliations:
School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907-1282, USA;School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907-1282, USA;Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA 02139-4307, USA;Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

This work presents new results for analysis of systems with repeated monotonic or slope restricted nonlinearities. We first give new integral quadratic constraints (IQCs) that are satisfied by the inputs and outputs of diagonal operators with equal, monotonic or slope restricted, diagonal entries. Then, we present new analysis results for systems with repeated nonlinearities, obtained using the new IQCs. For the type of nonlinearities considered in this work, the new results are less conservative than previously known results. The computation of the new conditions is discussed. The results in this paper apply also to problems with nonrepeated nonlinearities whenever these are representable as the interconnection of multiple repeated nonlinearities and a constant matrix.