A new design of robust H∞ filters for uncertain continuous-time stochastic systems

The robust H_∞ filtering problem for linear continuous-time stochastic systems with polytopic parameter uncertainties is studied in this paper, providing a methodology for its solution using a polynomial parameter dependent approach. The new linear matrix inequality (LMI) conditions obtained for the existence of admissible filters are developed based on homogenous polynomial parameter-dependent matrices of arbitrary degree. As special cases results the quadratic framework (using fixed matrices for the entire uncertain domain) and the linearly parameter-dependent framework (using linear convex combinations of matrices) are also solved. Numerical examples illustrate the effectiveness and advantages of the filter design methods proposed in this paper.