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In this paper, we consider state feedback robust control problems for discretetime nonlinear systems subject to disturbances. The objective of the control is to minimize a performance function while guaranteeing a prescribed quantitative input to state stability (ISS) property for the closed-loop systems. By introducing the concept of ISS control invariant set, a sufficient condition for the problem to be feasible is given. Built on the sufficient condition, a computationally efficient controldoi:10.3182/20080706-5-kr-1001.02405 fatcat:o53suvw7qzdcxjymfxlbbhhski