Finite-sample analysis of identification of switched linear systems with arbitrary or restricted switching

Abstract

This work aims to derive a data-independent finite-sample error bound for the least-squares (LS) estimation error of switched linear systems when the state and the switching signal are measured. While the existing finitesample bounds for linear system identification extend to the problem under consideration, the Gramian of the switched system, an essential term in the error bound, depends on the measured switching signal. Therefore, data-independent bounds on the spectrum of the Gramian are developed for globally asymptotically and marginally stable switched systems when the switching is arbitrary or subject to an average dwell time constraint. Combining the bounds on the spectrum of the Gramian and the preliminary error bound extended from linear system identification leads to the error bound for the LS estimate of the switched system.