Fractional Differential Equations

Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

Applications of Percolation Theory

Introduction to stochastic control

Estimation theory with applications to communications and control

This paper studies the impact of realistic wide-area measurement system (WAMS) time-varying delays on the dynamic behavior of power systems. A detailed model of WAMS delays including quasi-periodic, stochastic, and constant components is presented. Then, this paper discusses numerical methods to evaluate the small-signal stability as well as the time-domain simulation of power systems with inclusion of such delays. The small-signal stability analysis is shown to be able to capture the dominant modes through the combination of a characteristic matrix approximation and a Newton correction technique. A case study based on the IEEE 14-bus system compares the accuracy of the small-signal stability analysis with Monte Carlo time-domain simulations. Finally, the numerical efficiency of the proposed technique is tested through a real-world dynamic model of the all-island Irish system.

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Stability Analysis of Power Systems With Inclusion of Realistic-Modeling WAMS Delays

In this paper we are concerned with the solution of compressed sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend the primal-dual Newton Conjugate Gradient method (pdNCG) in [T. F. Chan, G. H. Golub, and P. Mulet, SIAM J. Sci. Comput., 20 (1999), pp. 1964--1977] to CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results are presented on CS problems which demonstrate the performance of pdNCG with the proposed preconditioner compared to state-of-the-art existing solvers.

A preconditioner for a primal-dual Newton conjugate gradients method for compressed sensing problems

In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend a primal-dual Newton Conjugate Gradients (pdNCG) method for CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results are presented on CS problems which demonstrate the performance of pdNCG with the proposed preconditioner compared to state-of-the-art existing solvers.

A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems

On non-homogeneous singular systems of fractional nabla difference equations

In this article, we study optimal solutions for a class of non-consistent singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. We take into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant. Then, first we study the system with given non-consistent initial conditions and provide optimal solutions. Furthermore, we consider the system with boundary conditions and provide optimal solutions for two cases, when the boundary value problem is non-consistent and when it has infinite solutions. Finally, we study the Kalman filter for singular non-homogeneous linear control systems of fractional nabla difference equations. Numerical examples are given to justify our theory.

Ioannis Dassios

Papers

Stability Analysis of Power Systems With Inclusion of Realistic-Modeling WAMS Delays

A preconditioner for a primal-dual Newton conjugate gradients method for compressed sensing problems

A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems

On non-homogeneous singular systems of fractional nabla difference equations

Optimal Solutions for Non-consistent Singular Linear Systems of Fractional Nabla Difference Equations