Investigation of stability of nonlinear continuous-discrete models of economic dynamics using vector Lyapunov function. I

Abstract

Modification and extension of procedures of strict analysis of stability and estimates of domains of attraction based on the reduction method with sublinear vector Lyapunov function is given for sufficiently wide class of nonlinear stabilization systems of continuous objects using piecewise constant control formed using discrete state measurements. The new type of realization of heterogeneous comparison systems in the form of interconnected differential and discrete impulse subsystems with varying right-hand side allowing to avoid preliminary discretization of the original system and thus increasing accuracy of investigations is proposed. In the case of nonlinearities (including those with respect to control and measurements), limited by semi-homogeneous functions. Constructive conditions of exponential stability with necessary quantitative estimates are formulated. Application to investigation of stability of economic growth in the Phillips-Bergstrom model with discrete monetary regulation is presented. The paper consists of two parts. In this part, the studied models are described, the studied stability property is defined, procedures for construction of vector Lyapunov function and comparison system are given, and some of their specific features are established.