Simona Petrakieva

Assessing the stability of linear time-invariant continuous interval dynamic systems

It is known that stability analysis of linear time-invariant dynamic systems under parameter uncertainties can be equated to estimating the range of the eigenvalues of matrices whose elements are intervals. In this note, first the problem of finding tight outer bounds on the eigenvalue ranges is considered. A method for computing such bounds is suggested which consists, essentially, of setting up and solving a system of n mildly nonlinear algebraic equations, n being the size of the interval matrix investigated. The main result of the note, however, is a method for determining the right end-point of the exact eigenvalue ranges. The latter makes use of the outer bounds. It is applicable if certain computationally verifiable monotonicity conditions are fulfilled. The methods suggested can be applied for robust stability analysis of both continuous- and discrete-time systems. Numerical examples illustrating the applicability of the new methods are also provided.

Interval criterion for stability analysis of discrete-time neural networks with partial state saturation nonlinearities

A generalization of sufficient conditions for global asymptotic stability of the equilibrium x/sub e/=0 of discrete-time neural networks, described by systems which have saturation nonlinearities on part of the states in the case of interval uncertainties, is considered. When using quadratic form Lyapunov functions, sufficient conditions, based on the positive definite interval matrices, are presented. In order to check this, a recent proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example, illustrating the applicability of the method suggested, is solved at the end of the paper.

Interval Raus criterion for stability analysis of linear systems with dependent coefficients in the characteristic polynomial

This paper addresses the stability analysis of linear continuous systems under interval uncertainties. An interval generalization of the known Raus criterion is suggested to estimate the stability of the system considered. It is based on obtaining the interval extensions of the elements of the Raus matrix which are nonlinear functions of independent system parameters. The case when these elements are independent intervals is considered. The interval extensions are also determined by using modified affine arithmetic. Two sufficient conditions on stability and instability of the linear system considered are obtained. A numerical example illustrating the applicability of the method suggested is solved at the end of the paper.

Application of neural networks, PCA and feature extraction for prediction of nucleotide sequences by using genomic signals

Converting symbolic sequences into complex genomic signals reveals surprising regularities of genomes, both locally and at a global scale. This approach allows using signal processing methods for the handling and analysis of nucleotide sequences, specifically for the prediction of nucleotides when knowing the preceding ones in the sequence. In this paper we propose both Feature Extraction (FE) and Principal Component Analysis (PCA) as methods to efficiently extract the major features of a genomic signal, using then a neural network to predict the next sample in the sequence.

Computer-Aided Education in Theoretical Electrical Engineering at the Technical University of Sofia: Part II

The paper shows the main areas of application of computer-aided education on theoretical electrical engineering in the Technical University of Sofia, Bulgaria. This part especially deals with the application of computers in course projects and is a continuation of the ideas given in the first part of the paper