Robust Performance and Observer Based Control for Periodic Discrete‐Time Uncertain Systems

Abstract

This paper presents an approach for the synthesis of observer-based controllers for discrete-time periodic linear systems. The H2 performance criterion has been employed to design both the observer and the controller. For the periodic observer design, two conditions in the form of Linear Matrix Inequalities (LMIs) are proposed, which stem from the Lyapunov Theory applied over the dynamics of the estimation error. The LMI condition obtained for the periodic state-feedback controller results from the application of the duality principle over the periodic system, under the assumption that only the estimated states are available to be used in the state-feedback compensation. Numerical experiments illustrate the potential of the proposed observer-based control technique.

Robust Eigenvalue Assignment via Sampled State-Feedback for Linear Polytopic Discrete-Time Periodic Systems

“…Examples of robust control techniques for this class of periodic systems include state and output-feedback design (De Souza and Trofino, 2000), state-feedback control with H 2 performance (Farges et al, 2007) and periodically time-varying memory state-feedback controller (Ebihara et al, 2011), which was extended for H ∞ synthesis (Trégouët et al, 2012). Recently, robust stability analysis conditions have been proposed for periodic systems with timevarying uncertainties (Agulhari and Lacerda, 2018) and observer-based control design for discrete-time uncertain periodic systems has been tackled by Agulhari and Lacerda (2019) and Keles et al (2019).…”