Subspace identification with guaranteed stability using constrained optimization

In system identification, the true system is often known to be stable. However, due to finite sample constraints, modeling errors, plant disturbances and measurement noise, the identified model may be unstable. We present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods. In subspace identification, we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters. To ensure asymptotic stability of the identified model, we write the least-squares optimization problem as a convex linear programming problem with mixed equality, quadratic, and positive–semidefinite constraints suitable for existing convex optimization codes such as SeDuMi. We present examples to illustrate the method and compare to existing approaches.