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Extended LMI characterizations for stability and performance of linear systems. (English) Zbl 1166.93014
Summary: Over the past ten years, extensive research has been devoted to extended Linear Matrix Inequality (LMI) characterizations for stability and performance of linear systems. These characterizations constitute a valuable tool for reducing conservatism in hard problems like multi-objective control, and robust stability and performance analysis. The present paper proposes a general, projection lemma based methodology for deriving such extended LMIs and hereby provides a straightforward and unified proof for all known literature results as well as some currently missing extended LMIs.

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C05 Linear systems in control theory
15A39 Linear inequalities of matrices
93D09 Robust stability
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