Generalisation of the Routh-Hurwitz criterion and its applications

Hwang, H. H.; Tripathi, P.C.

doi:10.1049/el:19700287

Cited by 12 publications

(5 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(ii) We need to show that the real part of the roots of C i must be less than 0. From [45] we know that the roots of a complex coefficient polynomial are in the left half plane if the roots of,…”

Section: Proof Of Lemmamentioning

confidence: 99%

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Gadjov

Pavel

2020

2020 59th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

In this paper, we consider distributed Nash equilibrium seeking in monotone and hypomonotone games. We first assume that each player has knowledge of the opponents' decisions and propose a passivity-based modification of the standard gradient-play dynamics, that we call "Heavy Anchor". We prove that Heavy Anchor allows a relaxation of strict monotonicity of the pseudo-gradient, needed for gradient-play dynamics, and can ensure exact asymptotic convergence in merely monotone regimes. We extend these results to the setting where each player has only partial information of the opponents' decisions. Each player maintains a local decision variable and an auxiliary state estimate, and communicates with their neighbours to learn the opponents' actions. We modify Heavy Anchor via a distributed Laplacian feedback and show how we can exploit equilibrium-independent passivity properties to achieve convergence to a Nash equilibrium in hypomonotone regimes. N j=1 w ij . Assume that W = W T so the weighted Laplacian of G is L = Deg − W . When G is connected and undirected, 0 is a simple eigenvalue of L, L1 N = 0, 1 T N L = 0 T , and all other eigenvalues are positive, 0 < λ 2 (L) ≤ • • • ≤ λ N (L).

show abstract

Section: Proof Of Lemmamentioning

confidence: 99%

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Gadjov

Pavel

2020

2020 59th IEEE Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…Obviously, the roots of (D.2) have negative real parts if and only if the roots of (D.1) have negative real parts [63]. Hence we can apply the Routh-Hurwitz criterion to the sixth-order polynomial (D.2) whose coefficients are real.…”

Section: Appendicesmentioning

confidence: 99%

Non-equilibrium, weak-field induced magnetism: a mechanism for magnetobiology

Matevosyan,

Allahverdyan

2021

Preprint

View full text Add to dashboard Cite

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a tiny (classically zero) equilibrium response. Second, the friction in the cellular environment is very large, preventing a weak field to alter non-equilibrium processes such as a free diffusion of charges. Here we study a class of non-equilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. In particular, such non-equilibrium states are generated by a white noise acting on the ion additionally to the (non-local) friction and noise generated by an equilibrium thermal bath.

show abstract

“…However, the same result, i.e., the confinement of all the roots in the aforementioned minor LHP sector (no roots in the corresponding major sector), had already been obtained well before by means of Routh-Hurwitz arguments (Usher, 1957;Luthi, 1942-43) or could easily have been achieved based on generalisations of the Routh-Hurwitz criteria (Hurwitz, 1895;Routh, 1877) to polynomials with complex coefficients (Frank, 1946;Billarz,1944). New formulations, extensions and improvements of similar algebraic conditions, including • the analysis of the critical cases and different tabular-form presentations, can be found in (Sivanandam & Sreekala, 2012;Chen & Tsai, 1993;Benidir & Picinbono, 1991;Agashe, 1985;Hwang & Tripathi; and, more recently, in (Bistritz, 2013) where numerically very efficient variants are presented . A different approach has been followed in (Kaminski et al, 2015) where, for q > 1, a test based on regular chains for semi-algebraic sets (Chen et al, 2013) has been suggested.…”

Section: Stability Conditionsmentioning

confidence: 99%

Fractional Order System Forced-response Decomposition and Its Application

Casagrande

Krajewski

Viaro

2018

Mathematical Techniques of Fractional Order Systems

View full text Add to dashboard Cite

This chapter deals with the additive decomposition of the forced response of a fractionalorder system. Precisely, it is shown how, by solving a simple polynomial Diophantine equation, this response can almost always be decomposed into the sum of a systemdependent component and an input-dependent component. The system-dependent component is formed from the same modes as the system and, assuming stabi li ty, characterises the transient behaviour of the system in the response to sustained inputs. The input-dependent component is formed from the same modes as the input, and accounts for the steady-state or long-term response of a stable system to a persistent input. Simple conditions based on the classical Routh and Mikhai lov criteria are provided to check the system input-output stability. Several examples show that the aforementioned decomposition can profitably be exploited to find simplified models in such a way that the asymptotic response is kept unchanged and, at the same time, the transient behaviour is well approximated. The decomposition proves useful also for solving the so-called model-matching problem that is of particular interest in controller synthesis.

show abstract

Generalisation of the Routh-Hurwitz criterion and its applications

Cited by 12 publications

References 1 publication

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

On the exact convergence to Nash equilibrium in monotone regimes under partial-information

Non-equilibrium, weak-field induced magnetism: a mechanism for magnetobiology

Fractional Order System Forced-response Decomposition and Its Application

Contact Info

Product

Resources

About