Imaginary-Axis Zeros in Multivariable H∞-Optimal Control
When a plant has jω-axis zeros or jω-axis poles, algorithms for computing H∞ -optimal control laws fail. Closely related problems arise with strictly proper plants; these plants may be interpreted as having jω-axis zeros at ω = ∞. These intrinsic problems with H∞ arise because the optimal control system has an irrational transfer function with point discontinuities on the jω-axis at the offending jω-axis zeros and poles of the plant. The difficulties with jω-axis poles and zeros are discussed and the methods for perturbing the H∞-problem to produce near-optimal rational control laws are proposed.
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