# Convergent dynamics of optimal nonlinear damping control

@article{Ruderman2021ConvergentDO, title={Convergent dynamics of optimal nonlinear damping control}, author={Michael S. Ruderman}, journal={ArXiv}, year={2021}, volume={abs/2106.00962} }

Following Demidovich’s concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking of C1-trajectories, it is shown that all solutions of the control system are globally uniformly asymptotically stable. The existence of the unique limit solution in the origin of the control error and its time derivative coordinates are shown in the sense of…

## References

SHOWING 1-10 OF 13 REFERENCES

Contractive Systems with Inputs

- Mathematics
- 2010

Contraction theory provides an elegant way of analyzing the behaviors of systems subject to external inputs. Under sometimes easy to check hypotheses, systems can be shown to have the incremental…

On Contraction Analysis for Non-linear Systems

- Mathematics, Computer ScienceAutom.
- 1998

These results may be viewed as generalizing the classical Krasovskii theorem, and, more loosely, linear eigenvalue analysis, and the approach is illustrated by controller and observer designs for simple physical examples.

Nonlinear Control Systems

- Computer Science
- 2008

Feedback control theory is concerned with the analysis and design of nonlinear control systems where nonlinearity plays a significant role, either in the controlled process (plant) or in the controller itself.

A Lyapunov approach to incremental stability properties

- Computer Science, MathematicsIEEE Trans. Autom. Control.
- 2002

The aim is to present a framework for understanding questions of incremental stability fully compatible with the well-known input-to-state stability approach.

Nonlinear Systems Analysis

- Computer Science, MathematicsIEEE Transactions on Systems, Man, and Cybernetics
- 1980

Non-linear Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and proof of the Frobenius Theorem.

Nonlinear Output Regulation: Theory and Applications

- Computer Science
- 2004

This chapter explains the development of a method for the nonlinear output regulation of singular nonlinear systems and some examples show how this regulation changed from linear to discrete-time systems over time.

Convergent dynamics, a tribute to Boris Pavlovich Demidovich

- Computer Science, MathematicsSyst. Control. Lett.
- 2004

Demidovich's approach forms a prelude to a field which is now called incremental stability of dynamical systems, and developments on incremental stability are reviewed from a historical perspective.

Nonlinear Systems

- 2013

Nonlinearity is ubiquitous in physical phenomena. Fluid and plasma mechanics, gas dynamics, elasticity, relativity, chemical reactions, combustion, ecology, biomechanics, and many, many other…

Lectures on the mathematical theory of stability

- Nauka, Moscow
- 1967