Robust stabilization with <i>H</i>_<i>∞</i> performance for a class of linear parameter‐dependent systems

We focus on the issue of robust stabilization with H ∞ performance for a class of linear time‐invariant parameter‐dependent systems under norm‐bounded nonlinear uncertainties. By combining the idea of polynomially parameter‐dependent quadratic Lyapunov functions and linear matrix inequalities formulations, some parameter‐independent conditions with high precision are given to guarantee robust asymptotic stability and robust disturbance attenuation of the linear time‐invariant parameter‐dependent system in the presence of norm‐bounded nonlinear uncertainties. The parameter‐dependent state‐feedback control is designed based on the Hamilton‐Jacobi‐Isaac (HJI) method. The applicability of the proposed design method is illustrated in a simple example.