The SVD System for First-Order Linear Systems

Abstract

This brief presents theoretical guarantees for stability and performance for the singular value decomposition (SVD) system with subsystems that are linear and first order. The SVD system reduces the dimension of the control input. It is used to meet the rank-one input constraint imposed by the row-column structure. The row-column structure reduces the number of inputs required to control mn subsystems to m + n. Although the subsystems are linear and first order, they can be dynamically coupled and are coupled nonlinearly by the SVD of the control input. Thus, the entire system is of order mn and nonlinear. Lyapunov stability and performance analysis demonstrates the effect of the SVD dimension reduction through comparisons to a system with full-rank inputs. The analysis also provides convenient methods for control design. Simulation examples demonstrate the use of the SVD system, theoretical results, and the SVD system's robustness with respect to noise and nonlinearities.