Robust H_∞ filtering for a class of time-delayed LPV systems

Based on the theory of robust H_∞ filtering, the problem of robust full-order H_∞ filtering for a class of continuous-time linear parameter-varying (LPV) systems with parameter-varying state delay is discussed. It is assumed that the state-space data and the time delay are dependent on the parameters that are measured in real-time and vary in a compact set with bounded variation rates. A parameter-dependent H_∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between the parameter-dependent Lyapunov functions and the system matrices. Then the corresponding linear parameter-dependent filtering design is presented. With sufficient conditions for the existence of admissible filter guaranteeing a desired H_∞ noise attenuation level is established in terms of parameterized linear matrix inequalities. The admissible filter can be found by solving a convex optimization problem with global convergence assured. A numerical example is given. Although the single delay case is considered, the results can be extended to treat multiple delays.