The estimation of the positive definite solutions to perturbed discrete Lyapunov equations is discussed. Several upper bounds of the positive definite solutions are obtained when the perturbation parameters are norm-bounded uncertain. In the derivation of the bounds, one only needs to deal with eigenvalues of matrices and linear matrix inequalities, and thus avoids solving high-order algebraic ...

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint diagonalization to low-rank and asymmetric matrices, and we also provide extensions to the perturbation analysis of these methods. Our results allow joint diagonalizati...

In this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. Iteration perturbation method leads us to high accurate solution. Two different high nonlinear examples are also presented to show the application and accuracy of the presented method. The results are compared with analytical methods and with the numerical solution using Runge-Kutta m...

<p class="Abstract"><span lang="EN-US">A novel online induction motor (IM) rotor time constant estimator based on a perturbation-based extremum seeking control (ESC) and model reference adaptive system (MRAS) is proposed. Since implementations of fieldoriented (FOC) requires accurate values IM parameters, such as constant, so robust on-line estimations parameters are crucial for any...

We formulate the importance sampling problem as a parametric minimization problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn’t depend on...