Geometric approach to robust stability analysis of Linear Parameter-Varying systems: Computational trade-offs between the exact and the simplex convex hulls

Igor P Vieira, Fernando O Souza and Leonardo A Mozelli

Applied Mathematics and Computation, 2023, vol. 451, issue C

Abstract: Robust stability is investigated for continuous-time, affine, Linear Parameter-Varying (LPV) models, with bounded variation rates of uncertainty. Towards this end, affine Parameter Dependent Lyapunov Functions (PDLF) are considered to certificate stability in the Lyapunov sense. In the literature, the search for PDLFs amounts to a non conservative Linear Matrix Inequality (LMI) problem, at expense of a factorial growth in its complexity. Remedies to overcome this complexity have been proposed recently, exploiting geometrical aspects of the problem, however, they can be conservative. This paper presents new stability tests that are a trade-off between the exact and the fastest solutions. We offer an analytical procedure to indicate when the proposed tests are prone to reduce conservativeness. Also, a simple procedure is introduced to possibly improve existing and new tests, without impacts on the computation effort. Numerical simulations illustrate the improvements of the proposed strategies.

Keywords: Linear parameter-varying systems; Parameter dependent lyapunov functions; Polytopic geometry; Computational effort (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:451:y:2023:i:c:s0096300323001868

DOI: 10.1016/j.amc.2023.128017

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