Scaled relative graphs for system analysis

@article{Chaffey2021ScaledRG,
  title={Scaled relative graphs for system analysis},
  author={Thomas Chaffey and Fulvio Forni and Rodolphe Sepulchre},
  journal={2021 60th IEEE Conference on Decision and Control (CDC)},
  year={2021},
  pages={3166-3172}
}
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output systems. It is shown that the Nyquist diagram of an LTI system on L2 is the convex hull of its scaled relative graph under a particular change of coordinates. The SRG may be used to visualize approximations of static nonlinearities such as the describing function… 

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References

SHOWING 1-10 OF 22 REFERENCES

Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry

Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a

Scaled Relative Graph of Normal Matrices

This work further study the SRG of linear operators and characterize theSRG of block-diagonal and normal matrices and views the SRGs as a generalization of the spectrum to multi-valued nonlinear operators.

Tight coefficients of averaged operators via scaled relative graph

Phase of Nonlinear Systems

The proposed nonlinear system phase, serving as a counterpart of $\mathcal{L}_2$-gain, quantifies the passivity and is highly related to the dissipativity, which possesses a nice physical interpretation which quantifying the tradeoff between the real energy and reactive energy.

System analysis via integral quadratic constraints

A stability theorem for systems described by IQCs is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality.

The gap metric: Robustness of stabilization of feedback systems

In this paper we introduce the gap metric to study the robustness of the stability of feedback systems which may employ not necessarily stable open-loop systems. We elaborate on the computational

Frequency response functions and Bode plots for nonlinear convergent systems

This paper extends frequency response functions defined for linear systems to nonlinear convergent systems, which give rise to non linear Bode plots, which serve as a graphical tool for performance analysis of nonlinear Convergent systems in the frequency domain.

An improved frequency time domain stability criterion for autonomous continuous systems

  • R. O'Shea
  • Computer Science
    IEEE Transactions on Automatic Control
  • 1967
A sufficient condtion given for the asymptotic stability of a system having a single monotonic nonlinearity with slope confined to 0 and a transfer function which corresponds to a nonzero time function for t, resulting in Z(j\omega) multiplier whose phase angle is capable of varying from +90° to -90° any desired number of times.

L2 Gain And Passivity Techniques In Nonlinear Control

L2 gain and passivity techniques in nonlinear control is downloaded for free to help people who are facing with some harmful virus inside their desktop computer.