Application of a Frequency-Discretization Technique for Stability and Control of Uncertain Differential Linear Repetitive Processes

The paper investigates the problem of stability analysis of differential linear repetitive processes with norm-bounded uncertainties. By applying a version of the Kalman-Yakubovich-Popov (KYP) Lemma, relaxed conditions for stability along the pass are proposed in terms of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. In particular, the conservatism of the resulting condition for stability along the pass can be significantly reduced by dividing the entire frequency domain into several sub-intervals and by applying KYP Lemma to each frequency sub-interval. Moreover, the obtained stability result is suitable for extension to robust control law design for processes with norm bounded uncertainty. Finally, a numerical example is provided to illustrate the application of the developed results.