Corpus ID: 119145608

On the existence and approximation of a dissipating feedback

@article{Guglielmi2018OnTE,
  title={On the existence and approximation of a dissipating feedback},
  author={Nicola Guglielmi and Valeria Simoncini},
  journal={arXiv: Optimization and Control},
  year={2018}
}
Given a matrix $A\in \R^{n\times n}$ and a tall rectangular matrix $B \in \R^{n\times q}$, $q < n$, we consider the problem of making the pair $(A,B)$ dissipative, that is the determination of a {\it feedback} matrix $K \in \R^{q\times n}$ such that the field of values of $A-B K$ lies in the left half open complex plane. We review and expand classical results available in the literature on the existence and parameterization of the class of dissipating matrices, and we explore new matrix… Expand
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References

SHOWING 1-10 OF 29 REFERENCES
Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations
  • V. Simoncini
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 2016
TLDR
It is shown that the Riccati approximate solution is related to the optimal value of the reduced cost functional, thus completely justifying the projection method from a model order reduction point of view. Expand
Finding the Nearest Positive-Real System
TLDR
This paper shows that a system is extended strictly PR if and only if it can be written as a strict port-Hamiltonian system, and uses a fast gradient method to obtain a nearby PR system to a given non-PR system. Expand
On the Minimization of Maximum Transient Energy Growth
TLDR
It is shown that by means of a Q-parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means a Ritz approximation of the free parameter. Expand
Robust port-Hamiltonian representations of passive systems
TLDR
This paper analyzes robustness measures for the different possible representations of stable and passive transfer functions in particular coordinate systems and relates it to quality functions defined in terms of the eigenvalues of the matrix associated with the LMI. Expand
The logarithmic norm. History and modern theory
In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities thatExpand
Port-Hamiltonian systems: an introductory survey
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systemsExpand
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
1 Introduction.- 2 State Space Representation.-3 Controllability of Finite-Dimensional Systems.- 4 Stabilizability of Finite-Dimensional Systems.- 5 Strongly Continuous Semigroups.- 6 Contraction andExpand
Mathematical Systems Theory I
TLDR
From these fruitful beginnings, research in controlled dynamical systems has experienced explosive growth in the intervening 40-plus years, resulting in a mature and well developed intellectual discipline with myriad and wide-ranging applications. Expand
Feedback Controller Norm Optimization for Linear Time Invariant Descriptor Systems With Pole Region Constraint
  • Subashish Datta
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • 2017
An algorithm is proposed to compute a state feedback gain matrix for a linear time invariant, regular descriptor system, which ensures that i) the closed loop system is impulse-free and ii) all theExpand
Matrix analysis
TLDR
This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. Expand
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