Logical Lyapunov functions for analysis of dynamic behavior of hybrid models of switching circuits

Concerns hybrid models which describe real processes in switching circuits more adequately than automata networks and more efficiently than mathematical physics models. The models consist of the following interconnected equations: differential, operational and logical equations, where from the physical viewpoint the first ones describe dynamics of internal states of circuit elements, the second ones correspond to the dynamics of output signals of the elements, and the latter ones describe their logical functions. In particular, each component of right-side of internal state equations can be dependent on states and outputs of all the elements, We propose some constructive and qualitative method of analysis of dynamical properties. This method reduces the initial problems to analysis of more simple, comparison model and does not require the exhaustive search for initial states, delay parameters, etc. and in principle, overcomes higher dimension of circuit in comparison with numerical methods of mathematical physics. Logical Lyapunov functions (LLF) are used, and not only those that are elementary disjunctions. Criteria of controllability-type properties contain more weak condition of majorizing the LLF than homomorphism condition, although they require the additional condition of quasimonotonicity of right-side of comparison model.