When does or does not circle criterion help in robust control synthesis for LTI systems with sector type nonlinearities?

Proposes regional L₂ performance analysis and synthesis methods for linear time invariant systems with sector type nonlinearities using the circle criterion. The methods can treat both nonzero initial state vectors of systems belonging to a bounded set and disturbance inputs belonging to a set of signals having bounded L₂ norm. We show that solvability of the synthesis problem can be checked by a linear matrix inequality (LMI) optimization problem if outputs of the nonlinear elements are measurable. Moreover, advantages of synthesis based on the circle criterion compared with a linear analysis are clarified especially in the case where the nonlinearities appear only in the control input parts