Robust H∞ filtering for uncertain 2-D continuous systems, based on a polynomially parameter-dependent Lyapunov function

The problem of robust H_∞ filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model is investigated when the parameter uncertainties are polytopic. A sufficient linear matrix inequality (LMI) condition for the existence of a 2-D continuous filter such that, for all admissible uncertainties, the error system is asymptotically stable, and the H_∞ norm of the transfer function from the noise signal to the estimation error is below a prespecified level. A sequence of standard LMI conditions that ensure the existence of homogeneous polynomially parameter-dependent (HPPD) matrices of arbitrary degree, that are solutions to the parameter-dependent LMIs is provided in terms of the vertices of the polytope. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases. Finally, an example is provided to demonstrate the effectiveness and advantages of the proposed filter design methodology.