Delay-Dependent H∞ Control of Linear Systems with Uncertain Input Delay Using State-Derivative Feedback

In some practical problems such as active vibration suppression systems, the state-derivative signals are easier to access than the state variables. This paper considers an H-infinity-based state-derivative feedback control problem for input-delayed systems. Applying this control law, the resulting closed-loop system turns into a specific time-delay system of neutral type. The significant specification of this neutral system is that its delayed term coefficients depend on the controller parameters. The time-delay is considered as uncertain time-invariant with a known constant bound. In this paper, the delay-dependent sufficient conditions for the existence of an H-infinity state-derivative feedback controller are derived in terms of matrix inequalities. The resulting H-infinity controller stabilizes the closed-loop neutral system and assures that the H-infinity-norm to be less than a prescribed level. An application example is presented to illustrate the effectiveness of the proposed method.