Abstract
Robust stability analysis of state space models with respect to real parametric uncertainty is a widely studied challenging problem. In this paper, a quite general uncertainty model is considered, which allows one to consider polynomial nonlinearities in the uncertain parameters. A class of parameter-dependent Lyapunov functions is used to establish stability of a matrix depending polynomially on a vector of parameters constrained in a polytope. Such class, denoted as Homogeneous Polynomially Parameter-Dependent Quadratic Lyapunov Functions (HPD-QLFs), contains quadratic Lyapunov functions whose dependence on the parameters is expressed as a polynomial homogeneous form. Its use is motivated by the property that the considered matricial uncertainty set is stable if and only there exists a HPD-QLF. The paper shows that a sufficient condition for the existence of a HPD-QLF can be derived in terms of Linear Matrix Inequalities (LMIs).
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Chesi, G., Garulli, A., Tesi, A., Vicino, A. An LMI-Based Technique for Robust Stability Analysis of Linear Systems with Polynomial Parametric Uncertainties. In: Henrion, D., Garulli, A. (eds) Positive Polynomials in Control. Lecture Notes in Control and Information Science, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10997703_5
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DOI: https://doi.org/10.1007/10997703_5
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Publisher Name: Springer, Berlin, Heidelberg
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