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Context-Aware systems are becoming useful components in autonomic and monitoring applications and the as- sessment of their properties is an important step towards reliable implementation, especially in safety-critical applications. In this paper, using an avalanche/landslide alert system as a running example, we propose a tech- nique, based on Boolean Control Networks, to verify that the system dynamics has stable equilibrium states, corresponding to constant inputs, and hence it does not exhibit oscillatory behaviors, and to establish other useful properties in order to implement a precise and timely alarm system. [ABSTRACT FROM AUTHOR]

For a positive switched system, the existence of a common linear copositive Lyapunov function (CLCLF) for the family of the subsystem matrices represents an important sufficient condition for its asymptotic stability. The main necessary and sufficient condition for the existence of a CLCLF (Fornasini and Valcher, IEEE Trans Autom Control 55:1933–1937, 2010, [1], Knorn et al, Automatica 45:1943–1947, 2009, [2]) consists in the explicit evaluation of the Hurwitz property of a family of pn matrices, where p is the number of subsystems and n the size of each subsystem. In this paper we show that, when restricting our attention to compartmental switched systems, the Hurwitz property may be checked on a smaller subset of smaller matrices. Based on this result, we provide an algorithm that allows to determine whether a CLCLF exists, by simply checking the column sums of matrix sets of increasingly lower dimension and cardinality. [ABSTRACT FROM AUTHOR]

In this study, the author investigates the input/output decoupling problem for Boolean control networks (BCNs). To keep up with the spirit of the original definition for linear state‐space models, that pertains the relationship between inputs and outputs independently of the state variables, two properties that formalise in different ways the idea that each single component of the output depends on the values of the corresponding input are provided, but not on the values of the other inputs. These properties are introduced by referring to the classical representation of a BCN in terms of Boolean input, state and output vectors, whose mutual relationships are expressed through the logical operators AND, OR and so on. In this set‐up, it is proven that there is some natural ordering among these properties, namely that one of them implies the other. In the second part of this study, it is shown that by resorting to the algebraic representation of BCNs a complete characterisation of these properties is possible. The algebraic characterisations obtained through this approach provide easy to check algorithms to evaluate whether a BCN is input/output decoupled or not. Finally, graph‐theoretic characterisations of the two input/output decoupling properties are provided. [ABSTRACT FROM AUTHOR]

In this chapter we investigate state-feedback and output-feedback stabilization of compartmental switched systems, under the additional requirement that the resulting switched system is in turn compartmental. Necessary and sufficient conditions for the solvability of the two problems are given. Subsequently, affine compartmental switched systems are considered, and a characterization of all the switched equilibria that can be ˵reached″ under some stabilizing switching law ]> is provided. [ABSTRACT FROM AUTHOR]

In this chapter the positive consensus problem for homogeneous multi-agent systems is investigated, by assuming that agents are described by positive single-input and continuous-time systems, and that each agent communicates with all the other agents. Under certain conditions on the Laplacian of the communication graph, that arise only when the graph is complete, some of the main necessary conditions for the problem solvability derived in [17–19] do not hold, and this makes the problem solution more complex. In this chapter we investigate this specific problem, by providing either necessary or sufficient conditions for its solvability and by analysing some special cases. [ABSTRACT FROM AUTHOR]

In this paper we study a generalized tracking and disturbance rejection problem for multidimensional behaviors. Given a multidimensional plant, our first goal is to design a compensator to be connected to the plant through regular partial interconnection, in such a way that the overall controlled system is autonomous and stable, when no exogenous signal acts on the system. On the other hand, when exogenous signals affect the controlled system evolution, we want to impose that a suitable linear combination of the overall system trajectories is "negligibile" in a sense we will clarify within the paper. This problem setup formalizes a number of classical control problems, first of all tracking of some (reference) signal together with rejection of another (disturbance) signal. The adopted approach is extremely general and it is based on the idea of describing all behavior trajectories as the sum of a "transient signal" and a "steady state" component, a decomposition that relies on Gabriel's localization theory. Necessary and sufficient conditions for the problem solvability are provided, and the compensators that satisfy the control goal are characterized in terms of an internal model condition. Furthermore, a parameterization of all such compensators is provided. [ABSTRACT FROM AUTHOR]

In this paper two-dimensional (2D) discrete behaviors, defined on the grid ℤ+ x ℤ and having the time as (first) independent variable, are investigated. For these behaviors, by emphasizing the causality notion that is naturally associated with the time variable, we introduce two new concepts of controllability. Algebraic characterizations of time-controllability and of zero-time-controllability are provided, and it is shown that behaviors endowed with these properties admit special decompositions. Next, the dead-beat control (DBC) problem and the concept of admissible DBC are introduced and related to the zero-time-controllability property. Differently from what happens with one-dimensional behaviors, zero-time-controllability does not ensure the existence of regular DBCs, and stronger algebraic properties need to be imposed on the behavior. Finally, necessary and sufficient conditions for the existence of a DBC that makes the resulting behavior both strongly autonomous and nilpotent are provided. [ABSTRACT FROM AUTHOR]

In this paper, monomial reachability and reachability properties for the special class of single-input discrete-time positive systems that switch among p subsystems, sharing the same state transition matrix, are investigated. Necessary and sufficient conditions for these properties to hold, together with some examples, are provided. [ABSTRACT FROM AUTHOR]

In this paper, dead-beat unknown input observers (UIOs) for two-dimensional (2D) state-space models are investigated. Dead-beat UIOs are observers which produce an exact estimate of the original system state trajectory, after a finite number of evolution steps, independently of the system and observer initial conditions and of the unknown disturbances that affect the system functioning. Necessary and sufficient conditions for the existence of dead-beat UIOs are provided, as well as a parameterization of all dead-beat UIO transfer matrices. Comparisons with Luenberger-type UIOs are also carried out, and the extension of the paper results to the case of asymptotic UIOs with a given rate of convergence and to Roesser models are finally discussed. [ABSTRACT FROM AUTHOR]

In this paper, the notions of simple, very simple and indecomposable autonomous behaviour are introduced and characterized. By resorting to some recent results about the direct sum decomposition of (linear, time-invariant, differential) behaviours (Bisiacco and Valcher 2001), as well as to the well-known primary decomposition theorem for finitely generated modules (Hartley and Hawkes 1970), it is shown that every autonomous behaviour can be expressed as a direct sum of indecomposable components, which are just cyclic modules of order p[sup v], for some irreducible polynomial p and some positive integer v. The non-uniqueness of this result is also discussed. Finally, this decomposition is interpreted in terms of modal analysis, and related to the results that can be obtained by mean of a state-space realization of the behaviour. [ABSTRACT FROM AUTHOR]

Nonnegative linear systems, which have traditionally been investigated within the state-space framework, have been recently introduced and analyzed by means of the behavioral approach. In a couple of recent papers [J. W. Nieuwenhuis, Linear Algebra Appl., 281 (1998), pp. 43-58, M. E. Valcher, Linear Algebra Appl., 319 (2000), pp. 147-162], several general definitions and results about nonnegative behaviors, as well as a complete analysis of nonnegativity property for autonomous behaviors, have been presented. In this contribution, by focusing our interest again on autonomous behaviors, we explore the nonnegative realization problem by deriving an extended set of necessary and sufficient (geometric) conditions for an autonomous behavior to be nonnegative realizable. In the scalar case, in particular, necessary and sufficient conditions for nonnegative realizability, which refer to the set of zeros of any polynomial involved in the kernel description of the behavior, are provided. Finally, a comparison between the nonnegative realizability property, here investigated, and K-realizability, addressed in [H. Maeda and S. Kodama IEEE Trans. Circuits, Systems I Fund. Theory Appl., CAS-281 (1981), pp. 39 47] is carried on. [ABSTRACT FROM AUTHOR]

Deals with a study which investigated the possibility of obtaining certain direct sum decompositions, for a given complete two-dimensional behavior, and proved to be equivalent to the zero skew-primeness property of suitable matrix pairs. Equivalent conditions for direct sum decomposition; Special cases and conclusion.

In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices that leave a proper polyhedral cone invariant [Trans. Amer. Math. Soc., 343 (1994), pp. 479–524] is given. The proof is a constructive one, as it allows us to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhedral cone Κ. Some new results are also presented, concerning the way A acts on the cone Κ. In particular, Κ-irreducibility, Κ-primitivity, and Κ-positivity are fully characterized. [ABSTRACT FROM AUTHOR]

Presents information on a study which described the characteristic cones and stability properties of two-dimensional autonomous behaviors of linear time-invariant systems. Description of the characteristic cones of autonomous behavior; Definition of stability for an arbitrary autonomous behavior; Conclusions.