H∞ fuzzy filtering design for non-linear sampled-data systems

The problem of H ^infin filtering design is studied for non-linear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. The sampled-data filtering is to estimate the states of a continuous-time system using only sampled measurements at discrete instants of time. Traditionally, the sufficient conditions for the existence of such an H ^infin filter are characterised in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequality with jumps. In general, there is no analytical solution for this non-linear partial differential inequality with jumps. First, in this study, the T-S fuzzy model is proposed to represent a class of non-linear sampled-data systems. Next, by using the T-S fuzzy model, the H ^infin fuzzy filtering design problem for non-linear sampled-data system is characterised in terms of a linear matrix inequality (LMI) problem. Hence, the H ^infin fuzzy filter of non-linear sampled-data systems can be given via solving LMIs instead of solving a differential Hamilton-Jacobi inequality with jumps. To illustrate the results, a numerical example is included.