CACSD using the state-space L∞ theory-a design example

The L^∞ optimal control theory is used to achieve singular value loop-shaping design objectives in a multivariable aircraft pitch-axis control design example involving an unstable nonminimum phase plant. Comparison to the frequency-weighted LQG (Linear quadratic Gaussian) design shows that the L^∞ theory easily produced a superior design having both higher bandwidth and greater stability margin, with no need for designer interaction for iterative adjustment of weights, than LQG. The design example provides a vivid illustration of how the all-pass property of the L^∞ theory enables precise shaping of closed-loop singular-value Bode plots to conform pointwise to prespecified weighting functions