Qualitative analysis of interconnected dynamical systems with algebraic loops: Well-posedness and stability

A qualitative analysis of a large class of dynamical systems endowed with algebraic loops is initiated. Such systems, viewed here as interconnected systems, arise naturally in many applications. Qualitative aspects considered include well-posedness (i.e., existence and uniqueness of solutions) as well as stability and instability in the sense of Lyapunov. Whenever appropriate, the analysis is accomplished at different hierarchical levels, namely, at the subsystem level and at the interconnecting structure level. To illustrate the applicability of the results, some specific examples are considered.