Abstract: This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
Abstract: Micro electromechanical sensors (MEMS) play a vital
role along with global positioning devices in navigation of
autonomous vehicles .These sensors are low cost ,easily available but
depict colored noises and unpredictable discontinuities .Conventional
filters like Kalman filters and Sigma point filters are not able to cope
with nonwhite noises. This research has utilized H∞ filter in nonlinear
frame work both with Kalman filter and Unscented filter for
navigation and self alignment of an airborne vehicle. The system is
simulated for colored noises and discontinuities and results are
compared with not robust nonlinear filters. The results are found
40%-70% more robust against colored noises and discontinuities.
Abstract: Robust nonlinear integrated navigation of GPS and
low cost MEMS is a hot topic of research these days. A robust filter
is required to cope up with the problem of unpredictable
discontinuities and colored noises associated with low cost sensors.
H∞ filter is previously used in Extended Kalman filter and Unscented
Kalman filter frame. Unscented Kalman filter has a problem of
Cholesky matrix factorization at each step which is a very unstable
operation. To avoid this problem in this research H∞ filter is
designed in Square root Unscented filter framework and found 50%
more robust towards increased level of colored noises.