Mixed $$\mathcal {H}_2/\mathcal {H}_{\infty }$$ H 2 / H ∞ Control for Time-Delayed Sampled-Data LPV Systems

A methodology for the synthesis of mixed $$\mathcal {H}_2/\mathcal {H}_{\infty }$$ controllers to stabilize delayed sampled-data LPV continuous-time systems is proposed in this paper. The technique consists of the resolution of a set of convex conditions for each considered norm, resulting in an appropriate gain-scheduling state-feedback gain guaranteeing the desired robustness and performance properties. The conditions are based on the application of Lyapunov–Krasovskii functionals, and an iterative algorithm is also proposed to enhance the norms minimization, thus reducing the conservatism of the technique. Numerical examples illustrate the validity of the method when compared to a similar technique in the literature.