Discrete-time mixed-norm H2/H∞ controller synthesis

H₂/H_∞ optimal control synthesis enables the design of controllers for simultaneous rejection of both narrow-band and wide-band disturbances and also has applications in robust control. Synthesis equations in the form of coupled Riccati and Lyapunov equations are available for both full-order and reduced-order, continuous-time H₂/H_∞ control design and it is possible to base numerical algorithm on these synthesis equations. However, currently it has not been found feasible to develop such synthesis equations for the equivalent discrete-time problems. This highlights the necessity of parameter optimization approaches for the design of discrete-time H₂/H_∞ controllers. This paper considers H₂/H_∞ discrete-time controller design and develops a zero-predictor continuation algorithm that uses quasi-Newton steps for correction. The algorithm is illustrated using a benchmark noncollocated flexible structure example.