Delay-Dependent Stabilization of Linear Input-Delayed Systems with Composite State-Derivative Feedback: Constant and Time-Varying Delays

This paper considers stability problem for inputdelayed systems for both constant and time-varying delay case. A new composite state-derivative control law is introduced, in which, a composition of the state variables and their derivatives appear in control law. By this means, the resulting closed-loop system becomes a particular time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the control law’s parameters. This condition provides new challenging issues which has its own merits in theoretical as well as practical aspects. In the present paper, new delay-dependent sufficient conditions are derived in presence of both constant and varying time-delay in terms of matrix inequalities. The resulting controllers guarantee asymptotic stability of the closed-loop system. Simulation studies are presented to verify the stability conditions obtained within the theorems.