Bivalent BAM theorem -Bivalent BAM theorem:every matrix is bidirectionally stable for synchronous or asynchronous state changes. Proof:consider the signal state changes that occur from time k to time k+1,define the vectors of signal state changes as: △S(X)=S(Xk+1)-S(Xk) =(AS(x)2…,ASn(xn),) AS(Y)=S(Y)-S(Y) =AS(y)2…,S,yp),） 55 Bivalent BAM theorem Bivalent BAM theorem: every matrix is bidirectionally stable for synchronous or asynchronous state changes. Proof: consider the signal state changes that occur from time k to time k+1,define the vectors of signal state changes as: ( ( ), , ( ),) ( ) ( ) ( ) 1 1 1 n n k k S x S x S X S X S X =    = + −  ( ( ), , ( ),) ( ) ( ) ( ) 1 1 1 p p k k S y S y S Y S Y S Y =    = + − 