MIMO H-infinity controller design for simultaneous guaranteed input and output stability margins

We consider completely controllable and observable plant described by: Plant: x = Ax + Bu, y = Cx; controller: u(s) = K(s)y(s). Find the transfer matrix of the output controller K(s), such that the following frequency inequalities are valid: [I + W^y (−jω)]^T [I + W^y (−jω)] ≥ r²I, [I + W^u (−jω)]^T [I + W^u (−jω)] ≥ r²I, where W^y and W^u are, respectively, output and control open-loop transfer matrices. The controller has the following form: xc = Acxc + Bcy, u = Ccxc + Dcy, xc ∊ R^nc with the associated transfer matrix K(s) = Cc (SI − Ac)⁻¹ Bc + Dc. To obtain a numerical solution to the problem, the method of linear matrix inequalities (LMI) is used.