Nearest stable system using successive convex approximations
(2013) Automatica — Vol. 49, n° 5, p. 1195-1203 (2013)
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- Stability is a crucial property in the study of dynamical systems. We focus on the problem of enforcing the stability of a system a posteriori. The system can be a matrix or a polynomial either in continuous-time or in discrete-time. We present an algorithm that constructs a sequence of successive stable iterates that tend to a nearby stable approximation X of a given system A. The stable iterates are obtained by projecting A onto the convex approximations of the set of stable systems. Some possible applications for this method are correcting the error arising from some noise in system identification and a possible solver for bilinear matrix inequalities based on convex approximations. In the case of polynomials, a fair complexity is achieved by finding a closed form solution to first order optimality conditions. © 2013 Elsevier Ltd. All rights reserved.
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Orban de Xivry, F.-X., Nesterov, Y., & Van Dooren, P. (2013). Nearest stable system using successive convex approximations. Automatica, 49(5), 1195-1203. https://doi.org/10.1016/j.automatica.2013.01.053 (Original work published 2013)