Robust control design for uncertain sampled data systems

The authors present a procedure for designing a full state feedback linear control law that guarantees stability of an uncertain sampled data system. A continuous-time system with matched time-invariant uncertainties in the system matrix is sampled at an interval T. A discrete linear controller that uses the sampled states is designed. The controller is designed neglecting O(T²) uncertainty terms in the discretized state space model. It is then verified that the system is stable for this choice of T with the O(T²) terms included. A sufficiently small positive T that assures stability is guaranteed to exist