State control design for discrete-time systems with state constraints

The paper examines the problem of state feedback control design, building on the dissipative principle and the slack matrix approach. Prescribing the system inputs to be less than or equal to defined bounds, the existence of feedback control law parameters is given in terms of the solvability of a set of linear matrix inequalities, ensuring in addition that the state variables will be constrained in ellipsoidal positive invariant set. Presented numerical examples illustrate practical validity and efficiency of the methodology.