A. K. Choudhury

Simplification of Incompletely Specified Flow Tables with the Help of Prime Closed Sets

In this short note, an attempt has been made to arrive at a general algorithm for minimizing the number of internal states in an incompletely specified flow table. The closure property of the compatibility classes which cover a given flow table leads us to the derivation of a particular class of closed sets defined as irredundant prime closed sets. It has been shown that these prime closed sets in sequential circuit synthesis play an analogous role to that of the prime implicants in combinational circuit synthesis. A method has been described for determining all the irredundant prime closed sets and finding the minimal row flow table by suitably choosing one or a collection of those sets.

On the decoupling of linear multivariable systems

In this paper we present a generalized approach to the decoupling problems of linear systems, such that both time-varying and time-invariant systems, scalar and block decoupling problems, may be studied in the same framework. We also derive the necessary and sufficient conditions for a linear system to be decoupled by output feedback only. Use of a state estimator, when some of the plant states are inaccessible, and the possibility of the reduction of its order are next studied. The results derived are illustrated by several examples.

Some Studies on Connected Cover Term Matrices of Switching Functions

ABSTRACT The central idea developed in the present paper involves the decomposition of the prime irnplicant covering problems of switching functions into the number of readily tractable sub-problems. It is shown that the minimizing function (Boolean representation of the prime implicant table) of a switching function can suitably be split up into a number of sub-functions such that the sum terms of each of these sub-functions can be arranged in any of the four possible distinct matrices called connected cover term matrices. The irredundant solutions of the sub-problem corresponding to each of the connected cover term matrices can be readily obtained, without the generation of a single redundant or duplicate solution, by following a systematic procedure suggested in the paper. The paper is concerned with the detailed study of the properties of the connected cover term matrices.

Transient stability of a power system by the second method of Lyapunov

The second method of Lyapunov has been applied to the transient stability analysis of a power system ; and the Lyapunov functions have been generated systematically by a method developed recently. The stability boundaries obtained have been compared with those obtained by other workers and have been found to give better results.

On the Determination of Irredundant Prime Closed Sets

The irredundant prime closed sets play an important role in the simplification of an incompletely specified flow table. In this note, an algebraic method for deriving the irredundant prime closed sets corresponding to any given flow table has been presented. It has been shown that the complete set of irredundant prime closed sets is obtained following the procedure suggested.

Complementary Function Approach to the Synthesis of Three-Level NAND Network

In the present paper efforts have been made to arrive at the three-level NAND network of any general Boolean function by utilizing its complementary function. It has been shown that the knowledge of the complementing gates of the three-level NAND circuit with minimum number of gates in the AND level can readily be obtained from the study of the prime implicants of the complementary function. A reduced form of the Cover and Closure (CC) table is suggested which is applicable in the above three-level NAND network synthesis. The paper also deals with the recognition of the class of functions for which the use of the CC table may be avoided to obtain the same network.

Maxterm Type Expressions of Switching Functions and Their Prime Implicants

One of the basic problems of combinational switching circuit theory is that of designing circuits with a minimum number of AND-gates or prime implicants. Algorithms have been formulated for this purpose which first generate all possible prime implicants corresponding to a specified switching function and then select minimal subsets of these prime implicants for use in the formation of the minimal networks [1]-[6]. In practically all the currently available methods of simplification of switching functions, use is made of the minterm type expression specified in the algebraic or its equivalent binary or decimal form. Operations with binary or decimal numbers have become very popular because of their inherent advantages.

An Iterative Array for Multiplication of Signed Binary Numbers

A simple method for the implementation of Booths algorithm for multiplication of signed binary numbers has been presented. It has been shown that for large word lengths, a significant economy has been achieved compared to Majithia and Kitais method.

On the decoupling of non-linear systems†

The problem of decoupling (diagonalization) of non-linear systems has been considered and an extension of the results of Porter (1970) has been obtained. The decoupling of non-linear multivariable differential systems is illustrated by threo examples.

On the evaluation of e Aτ

The purpose of this letter is to present a method for computing the transition matrix of linear time-invariant systems. Due to the important role the transition matrix plays in linear system response, several methods have been put forward for its computation. A numerical computation method, which avoids the use of the eigenvalues, for the evaluation of the transition matrix is presented here.