LPV control and analysis under uncertain initial conditions. (October 2021)

• Record Type: Journal Article
• Authors: Farhood, Mazen
• Is Part Of: Automatica. Volume 132(2021)
• Publication Date: 2021-10
• Subjects: Linear parameter-varying (LPV) systems -- Uncertain initial conditions -- Time-varying systems -- Eventually periodic systems -- Linear matrix inequalities (LMIs) -- Linear fractional transformation (LFT); Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109810
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper is focused on the control of discrete-time linear parameter-varying (LPV) systems with uncertain initial conditions. The synthesis objective is to design a feedback LPV controller that ensures that the closed-loop system is asymptotically stable and some performance inequality is satisfied for all permissible parameter trajectories. The performance measure used is similar to the ℓ 2 -induced norm except that the initial state and the disturbance input are considered to reside in two separate norm balls; that is, the supremum of the ℓ 2 -norm of the performance output is minimized subject to the initial state taking values in a unit Euclidean ball and the disturbance input taking values in a unit ℓ 2 -norm ball. The paper provides convex analysis and synthesis conditions for solving this problem and demonstrates that using nonstationary LPV controllers instead of standard LPV ones could result in a significantly improved performance. The paper also shows how to determine bounding envelopes for the performance output using the analysis result. An illustrative example concludes the paper.