State feedback robust dissipative control for singular systems with affine uncertainty

This paper mainly deals with the problem of state feedback robust dissipative control for singular systems with affine uncertainty. Firstly, a new description of the system uncertainty is obtained by converting it properly, based on which, the existence condition and explicit expression of a state feedback robust dissipative controller are derived by means of linear matrix inequalities(LMIs). However, the above condition may lead to great conservative result because it uses a single Lyapunov function matrix and includes no known information of the derivation of the uncertain parameters. Therefore, by using parameter-dependent Lyapunov function, the existence condition of a gain scheduling controller with less conservation is presented and the corresponding controller is constructed by using the solution of LMIs. Finally, the two conditions are analyzed and compared, and a numerical example is given to illustrate the effectiveness of the proposed conditions.