• Corpus ID: 237385225

Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems

@article{Mitchell2021RootmaxPH,
  title={Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems},
  author={Tim Mitchell and Paul Van Dooren},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.00974}
}
We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This problem is formulated for both continuous-time and discrete-time systems and is linked to the problem of finding a realization of a rational transfer function such that its passivity radius is maximized. Our new methods make use of the Hybrid Expansion-Contraction algorithm, which we extend and generalize… 
1 Citations

Figures and Tables from this paper

On properties of univariate max functions at local maximizers

More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum

References

SHOWING 1-10 OF 39 REFERENCES

Optimal Robustness of Port-Hamiltonian Systems

TLDR
It is shown that the realization with a maximal passivity radius is a normalized port-Hamiltonian one and its computation is linked to a particular solution of a linear matrix inequality that defines passivity of the transfer function.

FAST APPROXIMATION OF THE H∞ NORM VIA OPTIMIZATION OVER SPECTRAL VALUE SETS∗

TLDR
This work extends an algorithm recently introduced by Guglielmi and Overton for approximating the maximal real part or modulus of points in a matrix pseudospectrum to spectral value sets and introduces a Newton-bisection method to approximate the H∞ norm.

On properties of univariate max functions at local maximizers

More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum

Identification of Port-Hamiltonian Systems from Frequency Response Data

Optimal robustness of passive discrete time systems

We study different representations of a given rational transfer function that represents a passive (or positive real) discrete-time system. When the system is subject to perturbations, passivity or

How Near is a Stable Matrix to an Unstable Matrix

INEXACT NEWTON METHODS

A classical algorithm for solving the system of nonlinear equations $F(x) = 0$ is Newton’s method \[ x_{k + 1} = x_k + s_k ,\quad {\text{where }}F'(x_k )s_k = - F(x_k ),\quad x_0 {\text{ given}}.\]...

The generalized eigenstructure problem in linear system theory

TLDR
The numerical aspects of a certain class of such algorithms-dealing with what the author calls generalized eigenstructure problems-are discussed and some new and/or modified algorithms are presented.