Delay-dependent H∞ Variable Structure Control of Uncertain Singular Time-delay Systems: An LMI Approach

A delay-dependent H
∞
variable structure control is presented for uncertain singular time-delay systems. System with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances are considered. In terms of linear matrix inequalities (LMIs), we give a delay-dependent sufficient condition for the existence of switching surfaces, on which sliding mode dynamics is regular, impulse free, and internally asymptotically stable and satisfies H
∞
performance. We also give an explicit formula of such linear switching surfaces. A state feedback controller is derived to guarantee system trajectories convergent to the linear switching surface.