On the Construction of Diagonal Lyapunov Functions for Linear Systems

摘要

The paper generalizes the concept of diagonal-type Lyapunov functions for arbitrary H枚lder vector p-norms, 1驴p驴驴. For p = 2 this is equivalent with the usual quadratic form V(x)=xT驴x, where 驴 is a positive definite diagonal matrix, x is a real vector, and T denotes transposition. We provide concrete expressions for the Lyapunov function candidates that allow testing if a discrete- or continuous time system is asymptotically stable or not. These concrete expressions are constructed from the Perron or Perron-Frobenius eigenvectors of some matrices which either describe the system dynamics or majorize the matrices defining the dynamics.