Conditions of anisotropic norm boundedness for descriptor systems

Abstract

A class of systems, described by algebraic difference equations, is under consideration. Such systems are called descriptor (singular). For these systems the conditions of anisotropic norm boundedness are obtained. Anisotropic norm describes the root mean square gain of the system with respect to random Gaussian stationary disturbances, which are characterized by mean anisotropy. The conditions are formulated in the form of the theorem, detailed proof is given. Numerical example, illustrating anisotropic norm computation method for descriptor systems based of the proven theorem, is considered.