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We study the problem of approximating the joint spectral radius (JSR) of a finite set of matrices. Our approach is based on the analysis of the underlying switched linear system via inequalities imposed between multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class… (More)

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts – including ranking websites – and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of… (More)

- Raphaël M. Jungers, Francisca Zamorano, Vincent D. Blondel, Alain Vande Wouwer, Georges Bastin
- Automatica
- 2011

The concept of elementary flux vector is valuable in a number of applications of metabolic engineering. For instance, in metabolic flux analysis, each admissible flux vector can be expressed as a non-negative linear combination of a small number of elementary flux vectors. However a critical issue concerns the total number of elementary flux vectors which… (More)

- Francine Blanchet-Sadri, Raphaël M. Jungers, Justin Palumbo
- Theor. Comput. Sci.
- 2009

We prove that the problem of deciding whether a finite set of partial words is unavoidable is NP-hard for any alphabet of size larger or equal to two, which is in contrast with the well known feasability results for unavoidability of a set of full words. We raise some related questions on avoidability of sets of partial words.

— The question of knowing whether the Policy Iteration algorithm (PI) for solving stationary Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 25 years. Recently, an example on which PI requires an exponential number of iterations to converge was proposed for the total-reward and… (More)

- Paul Bell, Jean-Charles Delvenne, Raphaël M. Jungers, Vincent D. Blondel
- Theor. Comput. Sci.
- 2010

Keywords: Skolem-Pisot problem Exponential polynomials Continuous time dynamical system Decidability Ordinary differential equations a b s t r a c t We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of a linear recurrent sequence. In particular, we show that the… (More)

- Raphaël M. Jungers, Vincent D. Blondel
- Discrete Applied Mathematics
- 2011

An edge-colored directed graph is observable if an agent that moves along its edges from node to node is able to determine his position in the graph after a sufficiently long observation of the edge colors, and without accessing any information about the traversed nodes. When the agent is able to determine his position only from time to time, the graph is… (More)

The concept of elementary flux vector is valuable in a number of applications of metabolic engineering. For instance, in metabolic flux analysis, each admissible flux vector can be expressed as a non-negative linear combination of a small number of elementary flux vectors. However a critical issue concerns the number of elementary flux vectors which may be… (More)

- Vladimir Protasov, Raphaël M. Jungers, Vincent D. Blondel
- SIAM J. Matrix Analysis Applications
- 2010

We propose a new method to compute the joint spectral radius and the joint spectral subradius of a set of matrices. We first restrict our attention to matrices that leave a cone invariant. The accuracy of our algorithm, depending on geometric properties of the invariant cone, is estimated. We then extend our method to arbitrary sets of matrices by a lifting… (More)

- Julien M. Hendrickx, Karl Henrik Johansson, Raphaël M. Jungers, Henrik Sandberg, Kin Cheong Sou
- IEEE Trans. Automat. Contr.
- 2014

—The resilience of Supervisory Control and Data Acquisition (SCADA) systems for electric power networks for certain cyber-attacks is considered. We analyze the vulnerability of the measurement system to false data attack on communicated measurements. The vulnerability analysis problem is shown to be NP-hard, meaning that unless P = NP there is no polynomial… (More)