Robust H∞H∞ reduced order filtering for uncertain bilinear systems

This paper investigates both the H∞H∞ and robust H∞H∞ reduced order unbiased filtering problems for, respectively, a nominal bilinear system and a bilinear system affected by norm-bounded structured uncertainties in all the system matrices. First, an algebraic framework is used to solve the unbiasedness condition and second, a change of variable is introduced on the inputs of the system to reduce the conservatism inherent to the requirement of exponential convergence of the filter. Then the reduced order filtering solution is obtained through LMI with an equality constraint by transforming the problem into a robust state feedback in the nominal case and a robust static output feedback in the presence of uncertainties. In the last case, an additional bilinear matrix equality must also be solved.