## 1,128 Citations

On contraction analysis for hybrid systems

- MathematicsArXiv
- 2018

This work generalizes infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations.

Higher-Order Nonlinear Contraction Analysis

- Mathematics
- 2005

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem…

Contraction analysis: a practical approach to nonlinear control applications

- MathematicsProceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104)
- 1998

Contraction theory is a recently developed nonlinear analysis tool which may be viewed as an exact generalization of linear eigenvalues analysis. Based on a differential analysis of convergence, it…

Contraction analysis of non-linear distributed systems

- Mathematics
- 2005

Contraction theory is a comparatively recent dynamic analysis and non-linear control system design tool based on an exact differential analysis of convergence. This paper extends contraction theory…

Contraction methods for nonlinear systems: A brief introduction and some open problems

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

Contraction theory provides an elegant way to analyze the behaviors of certain nonlinear dynamical systems. Under sometimes easy to check hypotheses, systems can be shown to have the incremental…

On infinitesimal contraction analysis for hybrid systems

- Mathematics
- 2018

This work generalizes infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations and leverages an intrinsic distance function to derive the first contraction results for hybrid systems without restrictions on mode sequence or dwell time.

Contraction analysis for fractional-order nonlinear systems

- MathematicsChaos, Solitons & Fractals
- 2018

Generalizing infinitesimal contraction analysis to hybrid systems

- Mathematics, Engineering
- 2018

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological,…

Control system design for mechanical systems using contraction theory

- EngineeringIEEE Trans. Autom. Control.
- 2000

After establishing new combination properties of contracting systems, the paper derives new controller and observer designs for mechanical systems such as aircraft and underwater vehicles.

A Tutorial on Incremental Stability Analysis using Contraction Theory

- Mathematics
- 2010

A methodology for dierential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998) is introduced and the approach is illustrated on several simple examples.

## References

SHOWING 1-10 OF 25 REFERENCES

On metric observers for nonlinear systems

- MathematicsProceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro
- 1996

While observer design is well understood and widely used for linear systems, extensions to nonlinear systems have lacked generality. Motivated by fluid dynamics, this paper shows that the use of…

Applications of metric observers for nonlinear systems

- EngineeringProceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with IEEE International Symposium on Intelligent Contro
- 1996

The authors (1996) presented previously a new method for designing reduced order observers for nonlinear nonautonomous systems. This paper illustrates the design procedure in simulation for a variety…

Non-linear dynamical control systems

- Mathematics
- 1990

The controlled Invariant Submanifolds and Nonlinear Zero Dynamics and the Disturbance Decoupling problem are studied.

Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields

- Mathematics
- 1983

Contents: Introduction: Differential Equations and Dynamical Systems.- An Introduction to Chaos: Four Examples.- Local Bifurcations.- Averaging and Perturbation from a Geometric Viewpoint.-…

Applications of contraction analysis

- Computer ScienceProceedings of the 36th IEEE Conference on Decision and Control
- 1997

Contraction analysis may provide useful tools to analyze feedback controllers for biological motor control systems as combinations of simpler elements, or motion primitives, as this paper sketches.

Nonlinear Control Systems

- Mathematics
- 1985

The purpose of this book is to present a self-contained description of the fundamentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The…

Applied Nonlinear Control

- Computer Science
- 1991

Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive…

Mathematical Methods of Classical Mechanics

- Physics
- 1974

Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid…

Tensors, differential forms, and variational principles

- Mathematics
- 1975

A self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers and applied mathematicians is presented.