Algorithmic Approach to Abstracting Linear Systems by Timed Automata

Publication: Research - peer-review › Conference article in Journal

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Algorithmic Approach to Abstracting Linear Systems by Timed Automata. / Sloth, Christoffer ; Wisniewski, Rafael.

In: I F A C Workshop Series, 2011, p. 4546-4551.

Publication: Research - peer-review › Conference article in Journal

In: I F A C Workshop Series, 2011, p. 4546-4551.

Publication: Research - peer-review › Conference article in Journal

Bibtex

@article{a320f64ffb61417ba2a9cea8d0b53f65,

title = "Algorithmic Approach to Abstracting Linear Systems by Timed Automata",

publisher = "Elsevier Ltd. Books Division",

author = "Christoffer Sloth and Rafael Wisniewski",

year = "2011",

pages = "4546--4551",

journal = "I F A C Workshop Series",

issn = "1474-6670",

}

RIS

TY - CONF

T1 - Algorithmic Approach to Abstracting Linear Systems by Timed Automata

A1 - Sloth,Christoffer

A1 - Wisniewski,Rafael

AU - Sloth,Christoffer

AU - Wisniewski,Rafael

PB - Elsevier Ltd. Books Division

PY - 2011

Y1 - 2011

N2 - This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions. The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools.

AB - This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions. The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools.

U2 - 10.3182/20110828-6-IT-1002.02568

DO - 10.3182/20110828-6-IT-1002.02568

JO - I F A C Workshop Series

JF - I F A C Workshop Series

SN - 1474-6670

SP - 4546

EP - 4551

ER -