  In this work, a new two-stage identification method based on dynamic
programming and sparsity inducing is proposed for switched linear systems. Our
method achieves sparsity inducing in the identification of switched linear
systems by the constrained switching mechanism, in contrast to previous
optimization-based identification techniques that rely on the rigid data
distribution assumption in the parameter space. The proposed mechanism assumes
the existence of a minimal interval between adjacent switching instants. First,
an efficient iterative dynamic programming approach is used to determine the
switching instants and segments using the constrained switching mechanism.
Then, each submodel is identified as a combinatorial $\ell_0$ optimization
problem, and the true parameter for each submodel is determined by solving the
problem. The problem of combinatorial $\ell_0$ optimization is solved by
relaxing it into a convex $\ell_1$-norm optimization problem. Furthermore, the
unbiasedness of the switched linear system identification is discussed
thoroughly with the constrained switching mechanism and a new persistent
excitation condition is proposed. Simulation experiments are conducted to
indicate that our algorithms exhibit strong robustness against noise.
