Quasi-LPV Modeling and $H_\infty$ Gain-Scheduled State-Feedback Control Applied to a Control Moment Gyroscope

This article presents two contributions for addressing continuous-time linear parameter-varying (LPV) systems with parameters characterized by bounded variation rates. The first contribution introduces a novel procedure for designing a polynomial quasi-LPV model applicable to a class of nonlinear systems. This method takes into account multiple operating conditions and yields a quasi-LPV model suitable for addressing tracking problems without the need for the inclusion of integrators. The second contribution proposes a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> gain-scheduled state-feedback design condition. This technique is formulated using linear matrix inequalities in conjunction with a search for a bounded scalar parameter, which is beneficial for obtaining controllers that offer improved performance. Both the modeling and control design strategies are validated through practical applications involving a control moment gyroscope.