Matrix conditions for the stability of 2D dynamics
The stability of the 2D system \[ x(i,j)= A_1 x(i- 1,j)+ A_2 x(i,j- 1), \] where \(x(i,j)\in \mathbb{R}^n\), \(A_1,A_2\in \mathbb{R}^{n\times n}\) is analyzed. A new notion of stability of a pair of matrices is introduced. Necessary and sufficient conditions for the stability of the system are established. A condition for being free of overflow oscillations in saturation arithmetic is presented.
scientific article; zbMATH DE number 1513148