H∞ controller design for spectral MIMO models by convex optimization

A recent method for robust fixed-order H_∞ controller design by convex optimization proposed in [1] is investigated in this paper for the tuning of multivariable controllers. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a finite set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated 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. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. An application example illustrates the effectiveness of the proposed approach.