Robust ℋ∞ filtering for descriptor system with deterministic and stochastic uncertainties

This paper deals with the robust ℋ_∞ filter design to descriptor system subject to uncertain time-invariant parameters and stochastic perturbations. The uncertain parameters appear affinely in the matrices of the system state-space model and are assumed to belong to a given polytope, while the stochastic perturbations are described as multiplicative noises which affect the states and the measurement equations. For descriptor systems in differential algebraic representation, a LMI based method is proposed for designing linear stationary asymptotically stable filters which ensure the mean square stability and regularity of the estimation error dynamics and an optimized upper-bound on the ℒ₂-gain from the additive noise signal to the estimation error. The derived approach is based on parameter-dependent Lyapunov functions.