An LMI condition for robust stability of polynomial matrix polytopes

DOI10.1016/S0005-1098(00)00170-9zbMath0982.93057MaRDI QIDQ5930069

Michael Šebek, Didier Henrion, Dimitry Peaucelle, Denis Arzelier

Publication date: 9 April 2002

Published in: Automatica (Search for Journal in Brave)

zbMATH Keywords

robust stabilityquadratic stabilityLMI feasibilitypolynomial matrix polytopes

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Perturbations in control/observation systems (93C73) Robust stability (93D09)

Related Items

New results on robust stability and stabilization of linear discrete-time stochastic systems with convex polytopic uncertainties ⋮ LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties ⋮ Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties ⋮ On generalization of classical Hurwitz stability criteria for matrix polynomials ⋮ Positive polynomial matrices and improved LMI robustness conditions. ⋮ Robust stability criteria of Roesser-type discrete-time two-dimensional systems with parameter uncertainties ⋮ Stabilization of polytopes of plants by their vertices ⋮ Frequency domain criteria for robust \(\mathcal D\)-stability of MIMO systems based on LMI method ⋮ Unnamed Item ⋮ Robust model predictive control schemes for tracking setpoints ⋮ Unnamed Item ⋮ Sampling method for semidefinite programmes with non-negative Popov function constraints

Uses Software

• Matlab
• LMI toolbox
• Polynomial Toolbox
• Control System Toolbox
• PolyX

Cites Work

• Necessary and sufficient conditions for quadratic stabilizability of an uncertain system
• LMI characterization of structural and robust stability
• Fast projection methods for minimal design problems in linear system theory
• A new robust D-stability condition for real convex polytopic uncertainty
• A new discrete-time robust stability condition
• A sufficient condition for the stability of interval matrix polynomials
• On a Convex Parameter Space Method for Linear Control Design of Uncertain Systems
• Linear Matrix Inequalities in System and Control Theory
• H/sub ∞/ design with pole placement constraints: an LMI approach
• A survey of computational complexity results in systems and control
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