Dilated Matrix Inequalities for Control Design in Systems with Actuator Constraint

In this paper, we present a new variation of dilated matrix inequalities (MIs) for Bounded Real MI, invariant set MI and constraint MI, for both state and output feedback synthesis problems. In these dilated MIs, system matrices are separated from Lyapunov matrices to allow the use of different Lyapunov matrices in multi-objective and robust problems. To demonstrate the benefit of these new dilated MIs over conventional ones, they are used in solving controller synthesis problem for systems with bounded actuator in disturbance attenuation. It is shown that for the resulting multi-objective saturation problem, the new form of dilated MIs achieves an upper bound for $L_2$ gain that is less than or equal to the upper bound estimate achieved by conventional method.