A novel convex relaxation technique on affine transformed sampled-data control issue for fuzzy semi-Markov jump systems

This article investigates affine transformed sampled-data control problems for fuzzy semi-Markov jump systems (FSMJSs). First of all, in the novel fuzzy sampled-data control, an affine transformed membership function is introduced, which contributes to constructing the synchronous time scale grades of membership without any constraint condition. Then, by utilizing a mode-dependent Lyapunov function with the looped functions, a sufficient condition concerning the asymptotical stability of the closed-loop FSMJSs is established in the form of linear matrix inequality (LMI). Meanwhile, to solve parameterized LMI (PLMI), a novel convex relaxation technique is proposed, based on which less conservatism stabilization criteria of FSMJSs, and a maximum sampling interval with respect to sampled-data control are further derived. Finally, two examples are carried out to manifest numerically the validity of the raised method.