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

• Published in: Applied mathematics and computation 2023-08, Vol.451, p.128026, Article 128026
• Main Authors: Pan, X.Z., Huang, J.J., Lee, S.M.
• Format: Article
• Language: English
• Subjects: Affine matched premises; Convex relaxation technique; Fuzzy semi-Markov jump system; Parameterized linear matrix inequalities (PLMIs); Sampled-data control
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2023.128026

•This paper investigates affine transformed sampled-data control problems for fuzzy semi-Markov jump systems (FSMJSs).•To solve parameterized LMI (PLMI), a novel convex relaxation technique is proposed for a less conservative stabilization criteria of FSMJSs.•New mismatched PLMI with the proposed controller provides a larger region of the feasible solution compared to the non-affine membership function. 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.