"Lasserre, J.-B." . "For a linear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via quadratic-in-the-state Lyapunov functions polynomially dependent on the parameters. The contribution is twofold. First, if n denotes the system order and m the number of parameters, it is shown that it is enough to seek a parameterdependent Lyapunov function of given degree 2nm in the parameters. Second, it is shown that robust stability can be assessed by globally minimizing a multivariate scalar polynomial related with this Lyapunov matrix. A hierarchy of LMI relaxations is proposed to solve this problem numerically, yielding simultaneously upper and lower bounds on the global minimum with guarantee of asymptotic convergence." . . "Paucelle, D." . "New York" . "RIV/68407700:21230/04:03106388!RIV/2005/GA0/212305/N" . . . . "21230" . "P(GA102/02/0709), P(ME 698)" . . "On parameter-dependent Lyapunov functions for robust stability of linear systems" . . . "neuvedeno" . "4"^^ . . . "Henrion, Didier" . "Nen\u00ED k dispozici"@cs . "1"^^ . "[AFE4552D9E54]" . "Lyapunov functions; linear systems; robust stability"@en . "RIV/68407700:21230/04:03106388" . "On parameter-dependent Lyapunov functions for robust stability of linear systems"@en . . "Nen\u00ED k dispozici"@cs . . . "Arzelier, D." . . "On parameter-dependent Lyapunov functions for robust stability of linear systems" . "0-7803-8683-3" . "Nen\u00ED k dispozici"@cs . "On parameter-dependent Lyapunov functions for robust stability of linear systems"@en . . . . . "For a linear system affected by real parametric uncertainty, this paper focuses on robust stability analysis via quadratic-in-the-state Lyapunov functions polynomially dependent on the parameters. The contribution is twofold. First, if n denotes the system order and m the number of parameters, it is shown that it is enough to seek a parameterdependent Lyapunov function of given degree 2nm in the parameters. Second, it is shown that robust stability can be assessed by globally minimizing a multivariate scalar polynomial related with this Lyapunov matrix. A hierarchy of LMI relaxations is proposed to solve this problem numerically, yielding simultaneously upper and lower bounds on the global minimum with guarantee of asymptotic convergence."@en . "577780" .