Study of the stability of multidimensional systems using genetic algorithms

Mastorakis, NE; Gonos, IF

dc.contributor.author	Mastorakis, NE	en
dc.contributor.author	Gonos, IF	en
dc.date.accessioned	2014-03-01T01:48:47Z
dc.date.available	2014-03-01T01:48:47Z
dc.date.issued	1999	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/25593
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-4944221801&partnerID=40&md5=1d2a7f678fbe09d4734dffafec8231ff	en
dc.subject.other	Constraint theory	en
dc.subject.other	Functions	en
dc.subject.other	Genetic algorithms	en
dc.subject.other	Mathematical models	en
dc.subject.other	Polynomials	en
dc.subject.other	Problem solving	en
dc.subject.other	Theorem proving	en
dc.subject.other	Discrete variables	en
dc.subject.other	Multidimensional systems	en
dc.subject.other	Schur stability	en
dc.subject.other	System stability	en
dc.title	Study of the stability of multidimensional systems using genetic algorithms	en
heal.type	journalArticle	en
heal.publicationDate	1999	en
heal.abstract	The study of the Stability of m-dimensional systems is a difficult problem especially when m≥3. There exist only a few results and, unfortunately, there does not exist any practical criterion. In this brief, the stability of an m-dimensional system is dealt as a minimization problem of the absolute value of its characteristic polynomial over the boundaries of its variables (i.e. on the m unit circles). In this minimization, we seek for a global minimum. It is known that all the numerical algorithms and all the artificial neural networks' techniques can not guarantee the convergence to the total (global) minimum. On the contrary, genetic algorithms provide us the advantage of the convergence to the global minimum without the requirement of the differentiability nor of the objective function neither of the constraints. So, the problem of the stability of an m-D (multidimensional) system is reduced to a minimization problem of the absolute value of its characteristic polynomial over the boundaries of its variables which is solved via an appropriate genetic algorithm (GA). Numerical examples are presented.	en
heal.publisher	World Scientific and Engineering Academy and Society	en
heal.journalName	Computational Intelligence and Applications	en
dc.identifier.spage	29	en
dc.identifier.epage	36	en