Computation and Control pp 23-52 | Cite as

# Feedback Design from the Zero Dynamics Point of View

## Abstract

The development of a comprehensive feedback design methodology for nonlinear control systems, similar both in scope and in intuitive appeal to classical automatic control, is a long sought after goal in modern systems and control theory. The classical approaches to the control of finite dimensional linear systems made heavy use, in one or another form, of superposition properties of linear systems. In frequency domain terms, the response to fairly general input signals can be determined in terms of the superposition of the response to input sinusoids of arbitrary frequencies which can be conveniently encoded in terms of a frequency response, or transfer, function. Partial results, using “describing function” methods, similar in spirit to frequency domain methods, have been obtained for certain nonlinear systems; e.g., it is sometimes possible to estimate the frequency of a nonlinear oscillation using describing functions. Nonetheless, straightforward attempts to extend inherently linear properties, such as superposition, apply only in fairly special situations, falling far short of goals such as feedback stabilization, asymptotic tracking or disturbance attenuation for broad classes of nonlinear control systems.

## Keywords

Minimum Phase Nonlinear Control System Constant Rank Feedback Stabilization Zero Dynamic## Preview

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