ABSTRACT
For affine nonlinear delay-free stochastic systems, using an HJI-based SBRL, the H∞ and suboptimal mixed H2/H∞ filtering problems have been studied. A Nash game approach was applied to the suboptimal H2/H∞ filter design where the H2 performance is minimized in the presence of the worst-case disturbance. For a class of quasi-linear stochastic delay-free systems, the H8 filter design was presented in terms of LMIs. Moreover, a new H2/H∞ filter, for which the H2 performance index is taken as the error variance and is minimized when the disturbance is viewed as a white noise, has been investigated via a convex optimization technique. As extensions of the results of delay-free stochastic systems, HH∞ filtering for affine nonlinear and linear stochastic state-delayed systems has been studied, in particular, a useful moment estimate formula (Lemma) was obtained.
