A non-square sector condition and its application in deferred-action anti-windup compensator design

A sector condition for two connected deadzone nonlinearities is provided. By introducing an additional non-square operator which exploits their connectivity, a more general set of sector-like matrix inequalities is obtained. This “non-square” matrix inequality condition is applied to an anti-windup (AW) problem in which the AW compensator is not activated until the unconstrained control signal reaches a well-defined level beyond that of the physical actuator limits. The non-square sector condition allows such “deferred-action” AW synthesis to be performed in a manner much closer to traditional (“immediate”) sector-based AW with either lowered conservatism or decreased computational effort in contrast to recent work. The non-square condition is applicable to other AW problems.