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Effectiveness and limitation of circle criterion for LTI robust control systems with control input nonlinearities of sector type

This paper considers linear time invariant systems with sector type nonlinearities and proposes regional ℒ︁2 performance analysis and synthesis methods based on the circle criterion. In particular, we consider the effect of non‐zero initial states and/or an ℒ︁2 disturbance inputs on the ℒ︁2 norm of a selected performance output. We show that both analysis and synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for synthesis, the outputs of the nonlinear elements are assumed available for control. Moreover, it is shown when the circle criterion does or does not help to improve the performance bound in robust control synthesis when compared with the existing linear analysis method. Copyright © 2005 John Wiley & Sons, Ltd.