International Journal of Mathematics and Statistics Studies (IJMSS)

# Controllability

## Application of Non-Linear Evolution Stochastic Equations with Asymptotic Null Controllability Analysis (Published)

This paper investigated system of stochastic differential equations with prominence on disparities of drift parameters. These problems were solved analytical by adopting the Ito’s method of solution and three different investment solutions were obtained consequently. The necessary conditions were achieved which govern various drift parameters in assessing financial markets. Therefore, the impressions on each solution of investors in financial markets were analyzed graphically. Secondly, stock price data of Transco, LTD  were analyzed which covariance matrix were considered and analysis were logically extended to stochastic vector differential equation  where control measures were incorporated that would help in predicting different stock price processes, and the result obtained by exploring the properties of the fundamental matrix solution where asymptotic null controllability results were obtained by the singularity of the controllability matrix a function of the drift. Finally, the effects of the significant parameters of stochastic variables were successfully discussed.

## THE STRUCTURE OF INDICES OF CONTROL SYSTEMS FOR CERTAIN SINGLE – DELAY AUTONOMOUS LINEAR SYSTEMS WITH PROBLEM INSTANCES (Published)

This paper investigated the structure of indices of control systems for single – delay autonomous linear systems on the interval [0, 4h] and on [0, ∞) for special coefficient matrix cases, as well as provided a note on Euclidean controllability and application instances of the determination of their controllability dispositions.

The development of the associated control index matrices exploited the continuity of these matrices for positive time periods, change of variables technique, the method of steps and backward continuation recursions to obtain these matrices on successive intervals of length equal to the delay h.

The indices were derived using the stage – wise algorithmic format, starting from the right – most interval of length h. The structure could be gleaned and deciphered from the emerged sign convention and recognizable exponential integral ordering.

Keywords: Controllability, Index, Matrices, Method, Recursive, Steps.

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