New KYP lemma based stability tests and control law design algorithms for differential linear repetitive processes

This paper uses the Kalman-Yakubovich-Popov lemma to develop new stability tests for differential linear repetitive processes. The control systems theory for these processes have a number of applications areas and the new results in this paper also extend to the design of control laws. In comparison to currently available alternatives, these new tests offer the potential of reduced conservativeness by allowing the use of a Lyapunov matrix with piecewise constant entries as opposed to current algorithms where the Lyapunov matrix has constant entries. For control law design, linear matrix inequality formulations are developed that also extend to the practically relevant case where frequency attenuation is not enforced over the complete spectrum.