Pre‐filtering and post‐filtering in gain‐scheduled output‐feedback control

Abstract

Summary Linear matrix inequality (LMI) design conditions for gain‐scheduled output‐feedback H∞ control rely on assumptions constraining either system or controller matrices. Throughout the literature, it is common practice to avoid imposing restrictive assumptions on the controller, which may appear undesirable, in favor of state augmentations via pre‐filtering and post‐filtering to construct auxiliary augmented systems that comply with the alternative assumptions on the system matrices. This technique brings in the additional cost of increased state dimensions of the resulting gain‐scheduled output‐feedback controllers. In this paper, we explore the interplay and inherent trade‐offs between state augmentation, controller structure, and performance. We revisit LMI design conditions for quadratic output‐feedback H∞ control and demonstrate that state augmentation via pre‐filtering and post‐filtering in order to avoid constraints on the controller matrices is never advantageous even without taking into account the added complexity and propensity for numerical issues associated with state augmentation. As an additional contribution, we extend this observation to recently introduced modified LMI conditions allowing combined – however less restrictive – assumptions on system and controller matrices. Copyright © 2016 John Wiley & Sons, Ltd.

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

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Análisis y diseño de sistemas lineales con parámetros variamtes utilizando LMIs

“…que es un sistema LPV con matriz de entrada constante y por el cual la variabilidad asociada a B (θ(t)) queda incrustada en la matriz de estado. Sin embargo, cabe destacar que trabajos recientes han puesto en duda las ventajas aportadas por el filtro (46)-(47) respecto a usar directamente las LMIs (45) para el diseño del controlador (Pandey et al, 2016;Sehr and de Oliveira, 2017).…”