Robust ∞HControl of Uncertain Parameter-Dependent Systems

In this paper, we focus on the issue of robust disturbance attenuation and robust asymptotic stability problem for a class of parameter-dependent systems with norm bounded nonlinear uncertainties. By combining the idea of polynomial parameter-dependent quadratic functions and linear matrix inequalities (LMIs) formulations, a sufficient condition with high precision is given to guarantee robust asymptotic stability of the uncertain parameter-dependent systems. In the presence of the disturbance and norm-bounded nonlinear uncertainties, parameter-dependent state-feedback control is designed based on the Hamiltonian-Jacobi-Isaac (HJI) method. The applicability of the proposed design method is illustrated on a simple example.

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Index Terms- Linear matrix inequalities (LMIs) ، parameter-dependent systems ، robust stability ، disturbance attenuation