On attractive practical stability of the systems with state delay: A new algebraic inequalities approach

The attractive practical stability of the linear continuous control systems with time delay was investigated in this paper. The Lyapunov´s direct method was used to obtain the time-dependent conditions for the system stability. For this purpose, two matrix equations were presented: the matrix polynomial equation and the continuous algebraic Lyapunov matrix equation. The solution of the time delay differential equation was combined with the well-known Lyapunov approach to obtain the conditions for the attractive practical stability. Using this approach, we derived a sufficient novel delay-dependent condition for the practical stability of these control systems. As a result, the fulfillment of the stability conditions guarantees the attractivity of the system.