Finite-time Sample Complexity Analysis of Least Square Identifying Stochastic Switched Linear System

In this paper, we examine the high-probability finite-time theoretical guarantees of the least squares method for system identification of switched linear systems with process noise and without control input. We consider two scenarios: one in which the switching is i.i.d., and the other in which the switching is according to a Markov process. We provide concentration inequalities using a martingale-type argument to bound the identification error at each mode, and we use concentration lemmas for the switching signal. Our bound is in terms of state dimension, trajectory length, finite-time gramian, and properties of the switching signal distribution. We then provide simulations to demonstrate the accuracy of the identification. Additionally, we show that the empirical convergence rate is consistent with our theoretical bound.