Multi-objective robust H_∞ control for the delta operator formulated uncertain systems

The problem of robust H ∞ control for the delta operator formulated linear uncertain systems with circular pole constrains is studied. The state feedback controllers are designed such that the closed poles are located within a prespecified circular region, and the H ∞ norm of the closed-loop transfer function is less than a given positive scalar for all admissible uncertainties. By introducing the definition of quadratic D stabilizability with H ∞ norm-bound for delta operator systems, sufficient and necessary conditions and the corresponding state feedback control law are developed. The proposed results can be regarded as extensions of existing results on robust H ∞ control and robust pole assignment of delta operator uncertain systems.