NEW REMARK ON THE PROPERTIES OF STABLE INTERNAL CONTROL SYSTEMS OF A CERTAIN ORDER OF LINEAR DIFFERENTIAL EQUATIONS

The objective of this paper is to investigate and give sufficient and necessary conditions that guarantee the properties of stability of internal control systems for a certain order of Linear Differential Equations. This corresponds to globally exponentially stable equilibrium (point or position) of a system with input and output properties. We state and prove the classical Liapunov Theorem which allows us to reduce the stability analysis to an algebraic problem (computation of the eigenvalues of the matrix). We also introduce the quadratic Lyapunov functions and Lyapunov matrix equations that enhances the results of the defined objective. The Routh – Hurwitz criterion was given without proof. Since the results obtained in this study is different from the results and approach’s obtained in the literature, which implies that the results of this study are essentially new.