Nonsynchronized Robust Filtering Design for Continuous-Time T–S Fuzzy Affine Dynamic Systems Based on Piecewise Lyapunov Functions

This paper investigates the problem of robust
${\cal H}_{\infty}$
state estimation for a class of continuous-time nonlinear systems via Takagi–Sugeno (T–S) fuzzy affine dynamic models. Attention is focused on the analysis and design of an admissible full-order filter such that the resulting filtering error system is asymptotically stable with a guaranteed
${\cal H}_{\infty}$
disturbance attenuation level. It is assumed that the plant premise variables, which are often the state variables or their functions, are not measurable so that the filter implementation with state-space partition may not be synchronous with the state trajectories of the plant. Based on piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality linearization techniques, some new results are presented for the filtering design of the underlying continuous-time T-S fuzzy affine systems. Illustrative examples are given to validate the effectiveness and application of the proposed design approaches.