Abstract
The purpose of this paper is to analyze stability of the so-called particle swarm optimization (PSO) algorithm by modeling it as a Markov jump linear system with multiplicative noise, so that we can take into account the interaction between particles. A stability condition is represented in terms of linear matrix inequalities which is checked efficiently by using a convex optimization solver. A condition on the decay rate of the PSO algorithm is also shown. Stability region and contours of the decay rate of the PSO algorithm are shown by using the proposed analysis methods. Consequently, we provide more precise understandings of the PSO algorithm when the interaction between particles is considered.
