Kojima, Chiaki, Rapisarda, Paolo and Takaba, Kiyotsugu
Lyapunov stability analysis of higher-order 2D systems.
Multidimensional Systems and Signal Processing, 22, .
We prove a necessary and sufficient condition for the asymptotic stability of a 2D 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.
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