Static Iterative Learning Control Over Finite Frequency Domain for Actuator Failure Uncertain Systems

The main objective of this article is to investigate the stability and synthesis of controllers for discrete linear repetitive processes that exhibit polyhedral uncertainty. A condition is proposed, which utilizes a parameter-dependent Lyapunov function to alleviate conservatism resulting from uncertainty. The solution involves the use of a Lyapunov function that depends on uncertain parameters represented by a polyhedron, obtained through Linear Matrix Inequality (LMI) conditions. In practical scenarios, it is often the case that the frequency range of reference signals, noise, and interference is predefined, rendering full frequency range controller synthesis inadequate. To tackle this issue, we introduce a finite frequency controller using the generalized Kalman-Yakubovich-Popov (KYP) lemma. This approach enables designers to specify the desired control performance within a designated frequency range, which can be determined by analyzing the available signal spectrum.