Input-Output Data-Driven Stabilization of Continuous-Time Linear MIMO Systems
Haihui Gao, Alessandro Bosso, Lei Wang, David Saussié, Bowen Yi
TL;DR
This work tackles the problem of stabilizing continuous-time MIMO LTI systems directly from input–output data without assuming a uniform observability index. It leverages Kreisselmeier's adaptive filter as an observer for a canonical non-minimal realization of the plant, enabling an output-feedback controller that combines the filter with a linear state-feedback on the filter states. An LMIs-based data-driven synthesis procedure is developed, including a data-driven state decomposition to cope with rank-deficient data and a stabilization guarantee under stabilizability of the non-minimal realization. The approach yields a practical framework to compute stabilizing gains from trajectories, with numerical validation illustrating stable closed-loop behavior and spectral properties. This has potential impact for data-driven control in scenarios where full plant identification is impractical or observability indices are nonuniform.
Abstract
In this paper, we address the problem of data-driven stabilization of continuous-time multi-input multi-output (MIMO) linear time-invariant systems using the input-output data collected from an experiment. Building on recent results for data-driven output-feedback control based on non-minimal realizations, we propose an approach that can be applied to a broad class of continuous-time MIMO systems without requiring a uniform observability index. The key idea is to show that Kreisselmeier's adaptive filter can be interpreted as an observer of a stabilizable non-minimal realization of the plant. Then, by postprocessing the input-output data with such a filter, we derive a linear matrix inequality that yields the feedback gain of a dynamic output-feedback stabilizer.