A Lyapunov analysis of stability robustness for discrete linear descriptor systems

Discrete descriptor systems are those for which the dynamics are governed by a mixture of algebraic and difference equations. This paper examines the existence of solutions that are attracted by the origin of the phase space, for regular and irregular discrete linear descriptor systems. By a suitable transformation, the original system is transformed to a convenient form that enables development and easy application of Lyapunov's direct method for the existence analysis of a subclass of solutions characterized by convergence to the origin. A potential (weak) domain of attraction of the origin is underestimated on the basis of a symmetric positive definite solution of a reduced-order discrete Lyapunov matrix equations. Also, it has been shown that the same result can be efficiently used in determining quantitative measures of robustness for a class of perturbed discrete linear descriptor systems.