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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)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t The concept of elementary flux vector is valuable in a number of… (More)

An edge-colored directed graph is observable if an agent that moves along its edges is able to determine his position in the graph after a sufficiently long observation of the edge colors. When the agent is able to determine his position only from time to time, the graph is said to be partly observable. Observability in graphs is desirable in situations… (More)

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)

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 web-page ranking – and can be interpreted as the average portion of time spent at the node by an infinite random walk in the graph. We consider the problem of maximizing the PageRank of a node by… (More)

—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)

We study the synchronization phenomenon for deterministic finite state automata and the related longstandingČern´y conjecture. We formulate this conjecture in the setting of a two-player probabilistic game. Our goal is twofold. On the one hand, the probabilistic interpretation is of interest in its own right and can be applied to real-world situations. On… (More)