Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

10

${\mathcal{H}}_{\infty }$-Filtering for Singularly-Perturbed Nonlinear Systems

In this chapter, we discuss the counterpart filtering results for continuous-time singularly-perturbed affine nonlinear systems. The linear ${\mathcal{H}}_{\infty }$ filtering problem has been considered by a number of authors [178, 246], and the nonlinear problem for fuzzy T-S models has also been considered by a number of authors [39, 40, 41, 283]. This represents an interpolation of a number of linear models for the aggregate nonlinear system. Thus, the filter equations can be solved using linear-matrix inequalities (LMI) which makes the approach computationally attractive.

However, the general affine nonlinear filtering problem has only been recently considered by the authors [25, 26]. The results we ...