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Nearest stable system using successive convex approximations. (English) Zbl 1319.93062
Summary: 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.

##### MSC:
 93D09 Robust stability 65F30 Other matrix algorithms (MSC2010)
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##### References:
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