# Robustness of nonlinear control systems with respect to unmodeled dynamics

@article{Zhang1996RobustnessON, title={Robustness of nonlinear control systems with respect to unmodeled dynamics}, author={Youping Zhang and Petros A. Ioannou}, journal={Proceedings of 35th IEEE Conference on Decision and Control}, year={1996}, volume={1}, pages={315-320 vol.1} }

We examine the global stability properties of nonlinear controllers in the presence of high frequency unmodeled dynamics. We develop necessary and sufficient conditions for a general class of nonlinear control laws, under which global signal boundedess or asymptotic stability is guaranteed. We show that a wide class of nonlinear control laws does not satisfy these conditions and therefore does not guarantee global stability in the presence of high frequency unmodeled dynamics.

## 17 Citations

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## References

SHOWING 1-10 OF 18 REFERENCES

### Control of feedback linearizable systems with input unmodeled dynamics

- MathematicsProceedings of 1994 33rd IEEE Conference on Decision and Control
- 1994

A dynamic feedback design is proposed which guarantees global boundedness in the presence of input unmodeled dynamics at the input and applies to feedback linearizable systems, for which global asymptotic stability is also achieved.

### Robust control of strict- and output-feedback systems with input unmodeled dynamics

- MathematicsProceedings of 1995 34th IEEE Conference on Decision and Control
- 1995

Applies dynamic nonlinear damping to two classes of nonlinear systems: the strict-feedback systems where unmodeled dynamics affect all the "virtual inputs," and the output-feedback systems where the…

### Passive adaptive control of non‐linear systems

- Mathematics
- 1993

We develop a new recursive procedure for the design of adaptive controllers for non-linear systems with unknown parameters and unmeasured states. The use of novel nonlinear damping terms endows the…

### Design and Comparison of Globally Stabilizing Controllers for an Uncertain Nonlinear System

- Mathematics
- 1992

It is demonstrated how various integrator backstepping design procedures can be combined to produce new classes of stabilizing controllers for uncertain nonlinear systems.

### Robust Adaptive Control

- Mathematics1984 American Control Conference
- 1984

It is shown that if the persistent excitation of the reference input is larger than the perturbation in some sense, the solutions will be globally bounded.

### Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems,

- MathematicsAutom.
- 1993

### Robustification tools for nonlinear control design

- MathematicsProceedings of 1994 33rd IEEE Conference on Decision and Control
- 1994

We demonstrate the usefulness of the so-called /spl kappa/-terms as a robustification tool for nonlinear control. The inclusion of these terms in the design procedure renders the disturbance-to-state…

### Systematic Design of Adaptive Controllers for Feedback Linearizable Systems

- Mathematics1991 American Control Conference
- 1991

A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions,…

### Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions

- Mathematics1993 American Control Conference
- 1993