ℋ∞ Filtering for Polynomial Systems Over Switching Delayed Observations

The problem of designing an ℋ_∞ filter for a class of nonlinear polynomial systems over linear delayed observations is presented in this paper. Output observations may or may not experience sensor delay due to a random variable which is modelled as a Bernoulli distributed one which takes the quantities of zero and one. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the gain matrix. As a particular case, a third degree polynomial is considered to obtain the finite-dimensional filtering equations. Simulations results applied to an induction motor show the effectiveness of proposed filter.