On the Diagonal Stability of $k$-Positive Linear Systems

Chengshuai Wu; Michael Margaliot

On the Diagonal Stability of $k$-Positive Linear Systems

Dynamical Systems 2021-02-04 v2

Authors: Chengshuai Wu , Michael Margaliot

Abstract

We consider $k$ -positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to positive linear systems. It is well-known that stable positive linear time invariant (LTI) systems admit a diagonal Lyapunov function. This property has many important implications. A natural question is whether stable $k$ -positive systemsalso admit a diagonal Lyapunov function. This paper shows that, in general, the answer is no. However, for both continuous-time and discrete-time $n$ -dimensional systems that are $(n-1)$ -positive we provide a sufficient condition for diagonal stability.

Keywords

lyapunov stability stability theory lyapunov exponents

Cite

@article{arxiv.2003.09679,
  title  = {On the Diagonal Stability of $k$-Positive Linear Systems},
  author = {Chengshuai Wu and Michael Margaliot},
  journal= {arXiv preprint arXiv:2003.09679},
  year   = {2021}
}

Comments

We have updated this paper with a new title. Pls see search the new one titled as "Diagonal Stability of Discrete-time $k$-Positive linear Systems with Applications to Nonlinear Systems"

On the Diagonal Stability of $k$-Positive Linear Systems

Abstract

Keywords

Cite

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