Ponomarev's new method extends small-gain analysis to complex MIMO systems
Composing bounds iteratively lets engineers verify stability for previously intractable networks.
Anton Ponomarev's new paper on arXiv (2606.14745) adapts classical small-gain and small-phase stability analysis to modern MIMO (multiple-input multiple-output) LTI (linear time-invariant) subsystems. The key innovation is a 'composition of bounds' technique: starting from known parameters of individual subsystems — including phase sectors and the Crawford number — the method iteratively derives the same parameters for each consecutive interconnection (series, parallel, or feedback). This allows engineers to propagate bounds through complex network topologies.
The approach is demonstrated on three examples. Two are systems where traditional small-phase analysis cannot guarantee stability, yet Ponomarev's compositional method succeeds. The third example, while already solvable by classical methods, still benefits from the reduced computational overhead and clearer analytical framework. By composing gains of subsystems in the same manner, the method enables stability analysis of fairly complex systems that were previously intractable. For professionals in robotics, aerospace, and autonomous systems, this could mean faster and more reliable verification of large-scale control networks without sacrificing mathematical rigor.
- Compositional method iteratively bounds phase sectors and Crawford numbers across series, parallel, and feedback interconnections.
- Two example systems are shown to be tractable with this approach where classical small-phase analysis fails entirely.
- The technique composes gains of MIMO LTI subsystems, enabling stability verification for complex multi-loop control networks.
Why It Matters
Simplifies stability analysis for complex MIMO control systems, critical for autonomous vehicles and industrial robotics.