Vakif Dzhafarov

A novel approach to isolated word recognition

A voice signal contains the psychological and physiological properties of the speaker as well as dialect differences, acoustical environment effects, and phase differences. For these reasons, the same word uttered by different speakers can be very different. In this paper, two theories are developed by considering two optimization criteria applied to both the training set and the test set. The first theory is well known and uses what is called Criterion 1 here and ends up with the average of all vectors belonging to the words in the training set. The second theory is a novel approach and uses what is called Criterion 2 here, and it is used to extract the common properties of all vectors belonging to the words in the training set. It is shown that Criterion 2 is superior to Criterion 1 when the training set is of concern. In Criterion 2, the individual differences are obtained by subtracting a reference vector from other vectors, and individual difference vectors are used to obtain orthogonal vector basis by using the Gram-Schmidt orthogonalization method. The common vector is obtained by subtracting projections of any vector of the training set on the orthogonal vectors from this same vector. It is proved that this common vector is unique for any word class in the training set and independent of the chosen reference vector. This common vector is used in isolated word recognition, and it is also shown that Criterion 2 is superior to Criterion 1 for the test set. From the theoretical and experimental study, it is seen that the recognition rates increase as the number of speakers in the training set increases. This means that the common vector obtained from Criterion 2 represents the common properties of a spoken word better than the common or average vector obtained from Criterion 1.

The common vector approach and its comparison with other subspace methods in case of sufficient data

This paper presents an application of the common vector approach (CVA), an approach mainly used for speech recognition problems when the number of data items exceeds the dimension of the feature vectors. The calculation of a unique common vector for each class involves the use of principal component analysis. CVA and other subspace methods are compared both theoretically and experimentally. TI-digit database is used in the experimental study to show the practical use of CVA for the isolated word recognition problems. It can be concluded that CVA results are higher in terms of recognition rates when compared with those of other subspace methods in training and test sets. It is also seen that the consideration of only within-class scatter in CVA gives better performance than considering both within- and between-class scatters in Fishers linear discriminant analysis. The recognition rates obtained for CVA are also better than those obtained with the HMM method.

Common Lyapunov Functions for Some Special Classes of Stable Systems

In this work we consider the problem of existence and determination of a common positive definite solution (common quadratic Lyapunov function) to a set of Lyapunov matrix inequalities. We investigate a parameterized matrix family and a compact (in particular finite) set of 2 × 2 matrices.

FINITE-MONOTONICITY OF EIGENFUNCTIONS OF THE LAPLACIAN ON THE SIERPINSKI GASKET

We show that the restriction of an eigenfunction of the Laplacian on the Sierpinski Gasket (SG) to any segment inside the SG is monotone on finite pieces, i.e. there is a subdivision of the segment, such that the function is monotone on all subintervals.

On Stability of Parametrized Families of Polynomials and Matrices

The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices 𝒜 is equivalent to the nonsingularity of the family {𝐴2−2𝑡𝐴

Random search of stable member in a matrix polytope

Given a matrix polytope we consider the existence problem of a stable member in it. We suggest an algorithm in which part of uncertainty parameters is chosen randomly. Applications to affine families and 3 × 3 interval families are considered. A necessary and sufficient condition for the existence of a stable member is given for general interval families with nonnegative off-diagonal intervals.

On different types of stability of linear polytopic systems

Different types of stability of linear uncertain systems are considered. Stability conditions in terms of nonsingularity are obtained. Numerical examples of using the Bernstein expansion of the determinant function are given.

Stabilisation of discrete-time systems via Schur stability region

ABSTRACT In this paper, we consider the stabilisation problem of discrete-time systems by affine compensator. Using the known properties of the Schur stability region of monic polynomials, we give conditions under which stabilising controllers exist. A necessary and sufficient condition is obtained when the difference of the order of the system and the number of stabilising parameters is one. In the general case, two solution algorithms: division-elimination and least-square minimisation algorithms are suggested.

Discrete Time Stability Margins from Stein's Equation

This paper deals with the robust stability of a discrete time stable state space system subject to structured real parameter uncertainty. Using Lyapunovs Theorem and Steins equation the radius of a stability hypersphere in parameter space is derived from the structure matrices, with the property that all for parameter perturbations lying within the hypersphere stability of the system matrix is preserved. A numerical example is provided.

Diagonal Stability of Uncertain Interval Systems

In this paper we consider the problem of diagonal stability of interval systems. We investigate the existence and evaluation of a common diagonal solution to the Lyapunov and Stein matrix inequalities for third order interval systems. We show that these problems are equivalent to minimax problem with polynomial goal functions. We suggest an interesting approach to solve the corresponding game problems. This approach uses the opennes property of the set of solutions. Examples show that the proposed method is effective and sufficiently fast.