Subspace identification with eigenvalue constraints

Standard subspace methods for the identification of discrete-time, linear, time-invariant systems are transformed into generalized convex optimization problems in which the poles of the system estimate are constrained to lie within user-defined convex regions of the complex plane. The transformation is done by restating subspace methods such as the minimization of a Frobenius norm affine in the estimate parameters, allowing the minimization to be augmented with convex constraints. The constraints are created using linear-matrix-inequality regions, which generalize standard Lyapunov stability to arbitrary convex regions of the complex plane. The algorithm is developed for subspace methods based on estimates of the extended observability matrix and methods based on estimates of state sequences, but it is extendable to all subspace methods. Simulation examples demonstrate the utility of the proposed method.