In this project a new approach for robust fixed-order H infinity controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by a finite set of complex values in the frequency domain are considered. A sufficient condition for H infinity robust performance control is given by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be directly considered in the proposed approach by increasing the number of constraints.
For MIMO systems, it is shown that the Generalized Nyquist Stability criterion can be satisfied by a set of convex constraints with respect to the parameters of a multivariable linearly parameterized controller in the Nyquist diagram. Simultaneously, diagonal elements of the controller are tuned to satisfy the desired performances, while the off-diagonal elements decouple the system.