Distributed solver for linear matrix inequalities: an optimization perspective

Abstract

In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal-dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.

Synchronization of stochastic switching complex networks with a target of nonzero inputs

“…Although computational complexity will increase when the dimensions are increased, they can be calculated offline by using airborne equipments. Moreover, it is worth noting that some distributed approaches can be utilized to solve LMIs with large dimensions 46 …”

“…Moreover, it is worth noting that some distributed approaches can be utilized to solve LMIs with large dimensions. 46…”

Mean-square asymptotic synchronization of complex dynamical networks subject to communication delay and switching topology

“…Theorems 1 and 2, and Corollaries 1 and 2 provide different criteria for the synchronization of the CDNs in the form of matrix inequalities. In the case when the Jacobian matrix ( )  t is time-independent, and the coupling strength c and feedback gain l are fixed, these matrix inequalities become linear, enabling straightforward verification [38][39][40]. Notably, this allows us to estimate the range of the desired feedback gain based on the feasible solutions of the linear matrix inequalities.…”