Stability and absolute stability of a general 2-D non-linear FM second model [Brief Paper]

This study deals with the stability and absolute stability of the general 2-D non-linear time-invariant Fornasini-Marchesini (FM) second model. At first, a Lyapunov-type stability theorem is presented to sufficiently guarantee the stability and (globally) asymptotical stability of general 2-D non-linear FM second model. Then, for the globally asymptotical stability, it is further improved to lessen the conservatism of the stability theorem. More importantly, the improved theorem can derive global stability criteria which have the form of linear matrix inequalities. Furthermore, based on the two theorems, some absolute stability criteria are obtained for 2-D FM second model with sector-bounded non-linearity. Finally, three numerical examples show the advantage of the improved stability theorem.