Sufficient conditions guaranteeing Lyapunov stability, asymptotic stability and exponential stability of nonlinear two-dimensional continuous–discrete systems are proposed. Special attention is paid to neutrally stable systems such as some two-dimensional system descriptions of vehicle platoons, which may be stable or asymptotically stable but never exponentially stable. Our conditions for Lyapunov stability and asymptotic stability only require the corresponding two-dimensional Lyapunov function to have a negative semidefinite divergence. They are thus suitable for the analysis of non-exponential versions of 2D stability. Examples are given to illustrate the results.
['Steffi Knorn', 'Richard H. Middleton']
Asymptotic and exponential stability of nonlinear two-dimensional continuous–discrete Roesser models