Lyapunov stability analysis of higher-order 2-D systems

作者：Kojima C^*; Rapisarda P; Takaba K

来源：Multidimensional Systems and Signal Processing, 2011, 22(4): 287-302.

DOI：10.1007/s11045-010-0124-1

• 2-D system
• Lyapunov function
• Quadratic difference form
• Polynomial Lyapunov equation

In this paper we prove a necessary and sufficient condition for the asymptotic stability of a 2-D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra.

• 出版日期2011-12