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In this paper, we consider the agreement problem of a group of agents with nonlinear stochastic dynamics and each agent applies a local (distributed) nonlinear consensus protocol over random networks. We relate the almost sure consensus of agents under nonlinear consensus protocols to the stochastic semistability of nonlinear stochastic systems. We have proposed the notion of almost sure semistability...
This paper focuses on semistability and finite-time stability analysis and synthesis of systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we merge the theories of semistability and finite-time stability to develop a rigorous framework...
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