Subspace identification with guaranteed stability using constrained optimization

In system identification methods it is of interest to guarantee that the identified model is stable. To do this in the context of subspace identification methods we first obtain an estimate of the state sequence or extended observability matrix, then solve a least squares problem to estimate the system parameters. To ensure stability of the resulting model, we write the problem as a linear programming problem with mixed equality, quadratic, and positive semi-definite constraints. We present examples to illustrate the method and compare to existing approaches.