Guaranteed Stability with Subspace Methods
نویسنده
چکیده
We show how stability of models can be guaranteed when using the class of identification algorithms which have become known as ‘subspace methods’. In many of these methods the ‘A’ matrix is obtained (or can be obtained) as the product of a shifted matrix with a pseudo-inverse. We show that whenever the shifted matrix is formed by introducing one block of zeros in the appropriate position, then a stable model results. The cost of this is some (possibly large) distortion of the results, but in some applications that is outweighed by the advantage of guaranteed stability.
منابع مشابه
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 firs...
متن کاملStability criteria for Arnoldi-based model-order reduction
Pad e approximation is an often-used method for reducing the order of a nite-dimensional, linear, time invariant, signal model. It is known to suuer from two problems: numerical instability during the computation of the Pad e coeecients and lack of guaranteed stability for the resulting reduced model even when the original system is stable. In this paper, we show how the numerical instability p...
متن کاملConvergence of Restarted Krylov Subspace Methods for Stieltjes Functions of Matrices
To approximate f(A)b—the action of a matrix function on a vector—by a Krylov subspace method, restarts may become mandatory due to storage requirements for the Arnoldi basis or due to the growing computational complexity of evaluating f on a Hessenberg matrix of growing size. A number of restarting methods have been proposed in the literature in recent years and there has been substantial algor...
متن کاملSignal Decoupling with Preview: Perfect Solution for Nonminimum-phase Systems in the Geometric Approach Context
The problem of making the output insensitive to an exogenous input signal possibly known with preview is tackled in the geometric approach context. The definition of minimal preview for decoupling is introduced. Necessary and sufficient constructive conditions for decoupling with minimal preview are proved by means of simple geometric arguments. The structural and the stabilizability conditions...
متن کاملSparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on `1, `2 or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, `1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from diffe...
متن کامل