Exponential stability of 2-D systems (Q796481)

The exponential stability is defined for 2-D systems described by \((1)\quad x(r+1,s+1)=Ax(r,s+1)+Bx(r+1,s) r,s=0,1,..\). where \(x\in R^ n\) and A,B are \(n\times n\) real matrices. Necessary and sufficient conditions for exponential stability of (1) are given. It is shown that for (1) exponential stability and asymptotic stability are equivalent.