An orthonormal basis matrix $ X of a subspace {\mathcal X} is known not to be unique, unless there are some kinds normalization requirements. One them require that X^{ \text{T}}D positive semi-definite, where D constant apt size. It natural one in multi-view learning models which serves as projection and determined by maximization problem over the Stiefel manifold whose objective function conta...

Problems of the system identification using orthonormal functions are discussed and algorithms of computing parameters of the discrete time state-space model of the plant based on the generalized orthonormal functions and the Laguerre functions are derived. The adaptive LQ regulator and the predictive controller based on the Laguerre function model are also presented. The stability and the robu...

ui = Mvi ‖Mvi‖ = Mvi √ λi = Mvi σi Note that singular values σi are equal to √ λi; since M M is PSD, λi ≥ 0 and σi is well defined. In particular, observe that if M is a symmetric matrix, σi is the absolute value of the i-th eigenvalue of M . Now, we want to show that these vis and uis meet SVD conditions. Recall that vi’s are orthonormal because they are eigenvectors of MM , and uis are orthon...

In this paper we propose a new modeling technique for LTI multivariable systems using the generalized Orthonormal basis functions with ordinary poles. Once the model structure is built we proceed to update the membership set of the resulting model parameters through the execution of unknown but bounded error identification algorithms. This updating aims to synthesize a robust control strategy. ...