ABSTRACT
This chapter analyses the generalized KYP Lemma in the microactuator closed-loop design to suppress the narrow band disturbances. The KYP Lemma, being one of the most fundamental results in systems theory and control, establishes the equivalence between a frequency domain inequality for a transfer function and a linear matrix inequality associated with its state space realization. The generalized KYP Lemma gives a necessary and sufficient condition for a given transfer function to satisfy a required frequency domain property over a finite frequency range in terms of a matrix inequality condition. In the open loop comparison, the phase margin with the phase-lead peak filter method is much higher, while the bandwidth is lower and the gain margin is comparable with the KYP Lemma method. The system design problem with multiple specifications on the gain properties of the sensitivity function over several frequency ranges has been solved by the LMI optimization based on the KYP Lemma.
