Matrix comparison systems in the analysis of dynamics of control systems with structural changes

The method of matrix comparison systems is developed for examining dynamic properties and state estimation of control systems that are represented by nonlinear differential equations with structural changes and impulses. Comp arison theorems on stability, boundedness, and invariance of such systems a re obtained. Methods for constructing matrix comparison systems are elabora ted for nonlinear regulated systems with structural changes and impulses, w hich are used for obtaining estimates of behavior of sets of solutions star ting from a given ellipsoid. It is shown that a matrix comparison system de scribes the evolution of an ellipsoid that is an upper estimate of the reac hable set of the initial system, and a particular solution to the compariso n system defines a Lyapunov function that isolates an invariant set in the phase space. The results are illustrated by examining a control system with data unit faults or interruptions of receiving information from them.