2025/03/17 by Baron-Prada, Eder, Anta, Adolfo, Padoan, Alberto +1 · 4 citations
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2503.13367
We introduce a novel approach to feedback stability analysis for linear time-invariant (LTI) systems, overcoming the limitations of the sectoriality assumption in the small phase theorem. While phase analysis for single-input single-output (SISO) systems is well-established, multi-input multi-output (MIMO) systems lack a comprehensive phase analysis until recent advances introduced with the small-phase theorem. A limitation of the small-phase theorem is the sectorial condition, which states that an operator's eigenvalues must lie within a specified angle sector of the complex plane. We propose a framework based on Scaled Relative Graphs (SRGs) to remove this assumption. We derive two main results: a graphical set-based stability condition using SRGs and a small-phase theorem with no sectorial assumption. These results broaden the scope of phase analysis and feedback stability for MIMO systems.