H ∞ control of non-linear dynamic systems: a new fuzzy delay partitioning approach

The problem of robust H∞ control for Takagi–Sugeno (T–S) fuzzy systems with norm-bounded parameter uncertainties and a time delay in the state is investigated. Attention is focused on the design of robust H∞ controllers via the parallel distributed compensation scheme such that the closed-loop fuzzy time-delay system is asymptotically stable and the H∞ disturbance attenuation is below a prescribed level. By utilising the instrumental idea of delay partitioning, a new Lyapunov–Krasovskii functional is introduced, and some novel ideas for achieving delay dependence and basis dependence have been employed, which guarantee the obtained conditions to be much less conservative than most existing results in the literature. These conditions are formulated in the form of linear matrix inequalities (LMIs), based on which, the controller design is cast into a convex optimisation problem subject to LMI constraints. Finally, two examples are illustrated to show the feasibility and effectiveness of the obtained results.