Relaxed global asymptotic stability of 2-D state-space digital filters described by Roesser model with polytopic-type uncertainty

• The global asymptotic stability of uncertain 2-D state-space digital filters is obtained.
• The criterion takes the form of an LMI which is computationally tractable.
• A new Lyapunov function for 2-D state-space digital filters is proposed.
• A kind of matrix transformation technique is developed.

The problem of stability analysis of 2-D state-space digital filters described by Roesser model with parameter uncertainty is addressed in this paper. The underlying parameter uncertainty is modeled by a convex bounded (polytope type) uncertain domain. By applying both a new parameter-dependent Lyapunov function and a kind of matrix transformation technique, relaxed global asymptotic stability criteria of the 2-D state-space digital filters are proposed in terms of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. More importantly, the conservatism of the obtained global asymptotic stability criteria could be significantly reduced than existing ones. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.