An Input-Output Data-Driven Dissipativity Approach for Compositional Stability Certification of Interconnected LTI MIMO Systems

TL;DR

An input-output data-driven framework for certifying the stability of interconnected multiple-input-multiple-output linear time-invariant discrete-time systems via QSR-dissipativity by using measured input-output trajectories of each subsystem to verify dissipative properties and extract local passivity indices without requiring an explicit model identification.

Abstract

We propose an input-output data-driven framework for certifying the stability of interconnected multiple-input-multiple-output linear time-invariant discrete-time systems via QSR-dissipativity. That is, by using measured input-output trajectories of each subsystem, we verify dissipative properties and extract local passivity indices without requiring an explicit model identification. These passivity indices are then used to derive conditions under which the equilibrium of the interconnected system is stable. In particular, the framework identifies how the lack of passivity in some subsystems can be compensated by surpluses in others. The proposed approach enables a compositional stability analysis by combining subsystem-level conditions into a criterion valid for the overall interconnected system. We illustrate via a numerical case study, how to compute channel-wise passivity indices and infer stability guarantees directly from data with the proposed method.