Input-state-output representations and constructions of finite-support 2D convolutional codes

Two-dimensional convolutional codes are considered, with codewords having compact support indexed in N^2 and taking values in F^n, where F is a finite field. Input-state-output representations of these codes are introduced and several aspects of such representations are discussed. Constructive procedures of such codes with a designed distance are also presented. © 2010 AIMS-SDU

Composition codes

In this paper we introduce a special class of 2D convolutional codes, called composition codes, which admit encoders G(d1,d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1,d2)=G2(d2)G1(d1). Taking into account this decomposition, we obtain syndrome formers of the code directly from G1(d1) andG2(d2), in case G1(d1) andG2(d2) are right prime. Moreover we consider 2D state-space realizations by means of a separable Roesser model of the encoders and syndrome formers of a composition code and we investigate the minimality of such realizations. In particular, we obtain minimal realizations for composition codes which admit an encoder G(d1,d2)=G2(d2)G1(d1) withG2(d2) a systematic 1D encoder. Finally, we investigate the minimality of 2D separable Roesser state-space realizations for syndrome formers of these codes.publishe

Observability and Reconstructibility of Probabilistic Boolean Networks

Probabilistic Boolean Networks (PBNs) on a finite time interval are addressed. By assuming that the state update follows a probabilistic rule, while the output is a deterministic function of the state, we investigate under what conditions the knowledge of the output measurements in [0,T] allows the exact identification either of the initial state or of the final state of the PBN. By making use of the algebraic approach to PBNs, the concepts of observability, weak reconstructibility and strong reconstructibility are introduced and characterized. Set theoretic algorithms to determine all possible initial/final states compatible with the given output sequence are provided

On the bipartite consensus of higher-order multi-agent systems with antagonistic interactions and switching topologies

In this paper we, investigate the bipartite consensus of higher-order multiagent systems, by assuming that the interactions among agents are either cooperative or antagonistic and that the communication graph switches among a finite number of possible configurations.We first show that the \u201clifting approach\u201d, proposed in [3] to model opinion dynamics in case of antagonistic interactions and agents modeled as integrators, can be extended to the case of higher order multi-agent systems with cooperative/antagonistic interactions and switching topologies. Subsequently,we are able to translate the bipartite consensus problem into a consensus problem among cooperative agents with switching topologies. This allows us to make use of the results obtained in [13] and hence to solve the bipartite consensus problem

On the construction of matrix invariants with applications

Prague, Czech Republi

An algebraic approach to the construction of polyhedral invariant cones

Padova, Ital

Formal Verification of Context Aware Systems

This discussion paper introduces a modeling technique, based on Boolean Control Networks, for assessing useful properties of Context Aware systems. Indeed, Context Aware systems are becoming useful components in autonomic and monitoring applications and the assessment of their properties is an important step towards reliable implementation, especially in safety-critical applications

On the effects of communication failures in a multi-agent consensus network

This paper investigates the effects of either an edge or a node disconnection on a multi-agent consensus network, consisting of N agents that are modeled as simple scalar and discrete-time integrators. The communication among the agents is described by a weighted undirected graph. The first part of the paper addresses the case of an edge disconnection and summarizes the main results obtained in [29]. In particular, we show that if an edge disconnection does not affect the connectedness of the whole network, it does not even affect the final consensus value. Discernibility of the faulty network from the original one is investigated both in case the states of all the agents are available and in case only the states of a subset of the agents are available. Several equivalent conditions are derived and it is proved that the necessary and sufficient conditions for discernibility and for discernibility from the observation of a subset of agents are exactly the same and can be checked on the original state matrix and on its eigenvectors. The second part of the paper provides some original results about the effects of a node disconnection. In general, even when the connectedness of the remaining communication graph (namely the graph describing the interactions of the remainingN- 1 agents) is preserved, the network converges to a different consensus value. Also in this case, discernibility of the faulty network from the original one is investigated both in case the states of all the agents are available and in case only the states of a subset of the agents are available. Several equivalent conditions are provided to characterize both properties. Finally, a procedure to restore the original consensus value, after a node disconnection, is provided