Stability results for MIMO LTI systems via Scaled Relative Graphs

Abstract

This paper proposes a frequency-wise approach for stability analysis of multi-input, multi-output (MIMO) Linear Time-Invariant (LTI) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized Nyquist Criterion (GNC), which relies on a coupled analysis that requires the multiplication of models, our approach enables the evaluation of system stability in a decoupled fashion, system by system, each of which is represented by its SRG (or an over-approximation thereof), and it provides an intuitive, visual representation of system behavior. Our results provide conditions for certifying the stability of stable and square MIMO LTI systems connected in closed loop.