Lyapunov theory for nonstationary 2D systems

An extended Lyapunov theory is developed for checking the stability of nonstationary 2D digital filters. The development uses the wave model introduced by Porter and Aravena (1984). The analysis highlights the basic difficulty in stability studies for multidimensional systems. In utilizing the 1D nature of the wave model, the Lyapunov equations are time-variant, even for constant matrices in the Givone-Roesser model (Roesser, 1975). This time-variant characteristic invalidates the standard necessary and sufficient conditions available for stationary, 1D systems. However, it is shown that it is relatively straightforward to generate necessary or sufficient conditions.<>