  Stability and analysis of multi-agent network systems with state-dependent
switching typologies have been a fundamental and longstanding challenge in
control, social sciences, and many other related fields. These already complex
systems become further complicated once one accounts for asymmetry or
heterogeneity of the underlying agents/dynamics. Despite extensive progress in
analysis of conventional networked decision systems where the network evolution
and state dynamics are driven by independent or weakly coupled processes, most
of the existing results fail to address multi-agent systems where the network
and state dynamics are highly coupled and evolve based on status of
heterogeneous agents. Motivated by numerous applications of such dynamics in
social sciences, in this paper we provide a new direction toward analysis of
dynamic networks of heterogeneous agents under complex time-varying
environments. As a result we show how Lyapunov stability of several challenging
problems from opinion dynamics can be established using a simple application of
our framework. Moreover, we introduce a new class of asymmetric opinion
dynamics, namely nearest neighbor dynamics, and show how our approach can be
used to analyze their behavior. In particular, we extend our results to
game-theoretic settings and provide new insights toward analysis of complex
networked multi-agent systems using exciting field of sequential optimization.
