Fixed-structure discrete-time mixed H2/H∞ controller synthesis using the delta-operator

For discrete-time control, it has been shown that a difference operator formulation provides improved performance over the standard shift operator when using finite wordlength computation. This property has led to the use of the difference operator in several areas of modern multivariable control, including LQR/LQG and H^∞-optimal control. The discrete-time fixed-structure mixed H²/H^∞ problem has been formulated using the shift operator (q-domain) framework using both an H²/H^∞ norm overbound and a formulation of the exact constrained minimization problem. In both cases, the problem is nonconvex and thus requires a numerical algorithm for solution. The difference operator is applied to mixed H²/H^∞ controller synthesis. Necessary conditions for optimal mixed H²/H^∞ controller synthesis utilizing the difference operator are developed. Approximate solutions to these conditions are computed via a hybrid BFGS quasi-Newton/continuation algorithm, and compared with the solutions obtained from formulating the same problem in the q-domain.