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.