1,721,082 research outputs found
Algebraic Riccati equation and J-spectral factorization for H_infinity filtering and deconvolution
No full textThis paper deals with a general steady-state estimation problem in the H_infinity setting. The existence of the stabilizing solution of the related algebraic Riccati equation (ARE) and of the solution of the associated J-spectral factorization problem is investigated. The existence of such solutions is well established if the prescribed attenuation level g is larger than g_f (the infimum of the values of g for which a causal estimator with attenuation level g exists). We consider the case when g is less than or equal to g_f and show that the stabilizing solution of the ARE still exists (except for a finite number of values of g) as long as a fixed-lag a-causal estimator (smoother) does. The stabilizing solution of the ARE may be employed to derive a state-space realization of a minimum-phase J-spectral factor of the J-spectrum associated with the estimation problem. This J-spectral factor may be used, in turn, to compute the minimum-lag smoothing estimator. Some of the aspects of the J-spectral factorization problem and the properties of its solutions are discussed in correspondence to the (finite number of) values of g for which the stabilizing solution of the ARE does not exist
Effect of social influence on a two-party election: A Markovian multiagent model
Full text linkIn digital social networks, the filtering algorithms employed by the platform management to sieve the contents shared among the users can alter the social influence intensity. In this paper, a Markov multi-agent model of opinion dynamics is used to analyze possible opinion manipulation under apparently neutral interventions on the influence intensity. We consider a two-party election whose voters, modeled as heterogeneous agents, are connected in a social network with arbitrary topology. The equations describing the variance of the vote share, both in transient and steady state, are derived. The key is the solution of the second-order marginalization problem under the form of a numerically tractable characterization of pairwise joint probabilities of the voters' opinions. In particular, these probabilities are computed by means of a Lyapunov-like matrix differential equation driven by first-order moments. This result is used to answer some important questions, like the possible nonmonotonic effect of the influence intensity on the vote volatility and the interplay of topology and individuals' stubborness to determine the electoral balance between two parties
Stability, L 1 performance and state feedback design for linear systems in ice-cream cones
Full text linkThis paper considers linear systems which are positively invariant in a second-order cone (ice-cream cone). Three problems are addressed: (i) stability; (ii) L 1 performance; (iii) state feedback design for stabilisation and optimal L 1 performance while preserving cone invariance. We derive necessary and sufficient conditions via Linear Matrix Inequalities (LMI) for the solution of problems (i) and (ii). As for problem (iii), a full parametrization of feasible state feedback gains is provided, along with some LMI relaxations useful to compute a feasible gain. Finally, a numerical example is briefly discussed
Stochastic stability of Positive Markov Jump Linear Systems
No full textThis paper investigates on the stability properties of Positive Markov Jump Linear Systems (PMJLS's), i.e. Markov Jump Linear Systems with nonnegative state variables. Specific features of these systems are highlighted. In particular, a new notion of stability (Exponential Mean stability) is introduced and is shown to be equivalent to the standard notion of 1-moment stability. Moreover, various sufficient conditions for Exponential Almost-Sure stability are worked out, with different levels of conservatism. The implications among the different stability notions are discussed. It is remarkable that, thanks to the positivity assumption, some conditions can be checked by solving Linear Programming feasibility problems
On almost sure stability of continuous-time Markov jump linear systems
No full textIn this paper, we study the almost sure stability of continuous-time jump linear systems with a finite-state Markov form process. A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches. It is shown that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied. In order to evaluate the expected value appearing in the condition, an efficient Monte Carlo algorithm is worked out
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