Cleghorn, Christopher WesleyEngelbrecht, Andries P.2017-10-252018-03Cleghorn, C.W. & Engelbrecht, A.P. Particle swarm stability : a theoretical extension using the non-stagnate distribution assumption. Swarm Intelligence (2018) 12: 1-22. https://doi.org/10.1007/s11721-017-0141-x.1935-3812 (print)1935-3820 (online)10.1007/s11721-017-0141-xhttp://hdl.handle.net/2263/62934This paper presents an extension of the state of the art theoretical model utilized for understanding the stability criteria of the particles in particle swarm optimization algorithms. Conditions for order-1 and order-2 stability are derived by modeling, in the simplest case, the expected value and variance of a particle’s personal and neighborhood best positions as convergent sequences of random variables. Furthermore, the condition that the expected value and variance of a particle’s personal and neighborhood best positions are convergent sequences is shown to be a necessary condition for order-1 and order-2 stability. The theoretical analysis presented is applicable to a large class of particle swarm optimization variants.en© Springer Science+Business Media, LLC 2017. The original publication is available at : http://link.springer.comjournal/11721.Stability analysisStability criteriaParticle swarm optimization (PSO)Postprint Article