Reference:
S. Shi,
O. Mazhar, and
B. De Schutter,
"Finite-sample analysis of identification of switched linear systems
with arbitrary or restricted switching," IEEE Control Systems
Letters, vol. 7, pp. 121-126, 2023.
Abstract:
For the identification of switched systems with measured states and a
measured switching signal, this work aims to analyze the effect of
switching strategies on the estimation error. The data is assumed to
be collected from globally asymptotically or marginally stable
switched systems under switches that are arbitrary or subject to an
average dwell time constraint. Then the switched system is estimated
by the least-squares (LS) estimator. To capture the effect of the
parameters of the switching strategies on the LS estimation error,
finite-sample error bounds are developed in this work. The obtained
error bounds show that the estimation error is logarithmic of the
switching parameters when there are only stable modes; however, when
there are unstable modes, the estimation error bound can increase
linearly as the switching parameter changes. This suggests that in the
presence of unstable modes, the switching strategy should be properly
designed to avoid the significant increase of the estimation error.