Non-Lyapunov stability robustness consideration for discrete linear descriptor systems

Boundedness properties of dynamic response are particularly significant from the viewpoint of engineering applications. This paper examines some practically important properties of boundedness and unboundedness of regular and irregular discrete linear descriptor systems. The existence of specifically bounded solutions, as well as practical instability of these systems, are investigated. A development and simple application of Lyapunov's direct method for this analysis is presented. A potential (weak) domain of practical stability, consisting of points of the phase space which generate at least one solution with specific practical stability constraints, is underestimated. Also, it has been shown that the same theoretical results can be efficiently used in determining quantitative measures of robustness for a class of perturbed discrete linear descriptor systems.