A multiple-derivative and multiple-delay paradigm for decentralized controller design: uniform-rank systems

In this article, we introduce a promising methodology for designing stabilizing and high-performance yet practical topology-exploiting dynamic controllers for LTI decentralized systems, that is fundamentally based on 1) envisioning a control architecture with direct local feedback of multiple derivatives of the observation and 2) using multi-lead-compensator and multiple-delay control schemes to implement these multiple-derivative controllers. We show that this new signal-based methodology is capable of addressing many of the complexities that are common to modern decentralized systems, including very general observation topologies, saturation nonlinearities, and inherent network delays. In this installment, we motivate and introduce the design methodology for the wide class of (centrally) square-invertible uniform-rank plants. We focus on this class for three reasons: 1) because we have encountered decentralized plants with this structure in numerous infrastructural and sensing-agent networks, 2) to give an uncluttered presentation of the intricate design methodology, and 3) as a stepping-stone toward a design for general LTI decentralized plants.