Robust ℋ∞ and ℒ∞–ℒ∞ sampled-data dynamic output-feedback control for nonlinear system in T–S form including singular perturbation

This paper pays attention to the robust sampled-data dynamic output-feedback stabilisation problems for a singularly perturbed nonlinear system in Takagi–Sugeno (T–S) form when the system suffers from parametric uncertainties and $ \mathcal {L}_{2} $ L2 or $ \mathcal {L}_{\infty } $ L∞ disturbances. Two design conditions are proposed in terms of linear matrix inequalities such that the admissible controllers guarantee the prescribed $ \mathcal {H}_{\infty } $ H∞ and $ \mathcal {L}_{\infty } $ L∞– $ \mathcal {L}_{\infty } $ L∞ disturbance-attenuation levels, respectively. The features of the development are that (i) the sampled-data syntheses are performed in a continuous-time domain and (ii) (even approximate) discrete-time modelling of the T–S fuzzy system is not involved.