Robust control with finite frequency specification for uncertain discrete linear repetitive processes
This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes withpolytopic uncertainty. In therobust control domain, conditions based on parameter dependent Lyapunov functions are proposed inorder toreduce theconservatism related to uncertainty problems. The solution is a class ofLyapunov functions that depends in apolytopic way on theuncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range ofreference signals, noises anddisturbances are known beforehand. Therefore, performing controller synthesis in thefull frequency range is not practically suited and may introduce conservatism tosome extent. Based on generalized KalmanYakubovichPopov Lemma, afinite frequency controller is derived for uncertain discrete linear repetitive processes which are themost investigated class of2D systems. Hence, thedesigner can specify afrequency range where theprescribed control performance is required, where, for example, this range could be determined by inspection offrequency spectrums oftheavailable signals.
linear repetitive processes kalmanyakubovichpopov lemma parameter-dependent lyapunov functions