The article provides a comparative analysis of approaches, methods and formalized mathematical descriptions used to assess the functional stability of heterogeneous information systems. Features and criteria of functional stability are considered. The definitions of the concepts of functional stability, heterogeneous information systems, indicator and criterion of functional stability are given. The difference between the concepts of stability of functioning and functional stability of complex technical systems is indicated. Formalized descriptions of the structural and probabilistic criteria for the functional stability of the structure of a heterogeneous information system are given. The mathematical formalization of the functional stability indicator for structures with serial and parallel connection of elements is given. The indicator of the structural complexity of the data transmission system of the automated air traffic control system is mathematically formalized. The article presents a method for assessing the functional stability of an automated air traffic control system and a method for calculating a generalized probabilistic indicator of functional stability as a convolution of the structure connectivity matrix. The directions of further research on the assessment of the functional stability of heterogeneous information systems are determined.