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In this study, the issue of simultaneous fault detection and control (SFDC) for a class of switched linear systems with input and state delays is being addressed. A detector/controller unit (dynamic observer/observer-based controller) is suggested for a residual generation that simultaneously takes into account the control and fault detection objectives using specific performance indices. It is assumed that the delay will fluctuate within a range with a lower bound that is not zero. Based on a Lyapunov–Krasovskii functional (LKF), and thanks to the free-weighting matrix and projection lemma, a new sufficient condition for developing a new method is put forth in terms of a set of linear matrix inequalities (LMIs). To illustrate how well the suggested results work, the proposed method is applied to a vehicle roll dynamic. [ABSTRACT FROM AUTHOR]

This paper presents a detailed investigation of both normal and intruder states in 98Mo nucleus in the E ≥ 3 MeV. We considered all reported intruder energy levels for this nucleus, 0+2, 2+1, 4+1, 4+2, 2+2, and also the quadrupole transitions which originated from these levels. A mixing formalism based on the combination of U(5) and O(6) dynamical symmetries of the interacting boson model is used in the Hamiltonian and wavefunctions for, respectively, N- and (N + 2)-boson spaces. The weight of each space is determined by the calculation of theoretical quadrupole transition rates and compared with their experimental counterparts. By using these weights, the expectation values of the pure U(5) and O(6) Hamiltonians and also the total Hamiltonian that contains these limits and mixing terms are calculated for different levels, too. The results show that normal energy levels and quadrupole transition between them can be described satisfactory in comparison with experimental counterparts by using the pure U(5) Hamiltonian in the only N-boson space. For intruder levels and quadrupole transition originating from them or holding between normal and intruder states, the mixed formalism of Hamiltonian and wavefunctions increases the efficiency of theoretical formalisms and suggests exact results. [ABSTRACT FROM AUTHOR]

Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative protocols, which consist of multiple agents that are coupled together via an undirected state-dependent graph. We develop a representation of the system solution by decomposing the nonlinear system utilizing ideas from the Koopman operator theory and its spectral analysis. We use recent results on the extensions of the wellknown Hartman theorem for hyperbolic systems to establish a connection between the original nonlinear dynamics and the linearized dynamics in terms of Koopman spectral properties. The expected value of the output energy of the nonlinear protocol, which is related to the notions of coherence and robustness in dynamical networks, is evaluated and characterized in terms of Koopman eigenvalues, eigenfunctions, and modes. Spectral representation of the performance measure enables us to develop algorithmic methods to assess the performance of this class of nonlinear dynamical networks as a function of their graph topology. Finally, we propose a scalable computational method for approximation of the components of the Koopman mode decomposition, which is necessary to evaluate the systemic performance measure of the nonlinear dynamic network. [ABSTRACT FROM AUTHOR]

Let (I , A) be a pair of n -Lie algebras. Then, we introduce the concept of Schur multiplier of the pair (I , A) , denoted by ℳ (I , A) , and some inequalities for the dimension of ℳ (I , A) are given. We also determine a necessary and sufficient condition, for which the Schur multiplier of a pair of n -Lie algebras can be embedded into the Schur multipliers of their n -Lie algebra factors. Moreover, some inequalities for the Schur multiplier of a pair of finite-dimensional nilpotent n -Lie algebras are acquired. [ABSTRACT FROM AUTHOR]

Abstract: The main objective of fault tree analysis method is to estimate the “Top Event occurrence probability”. This requires determination of failure time distribution functions also known as “Bathtub Curves” for each of the system elements/events. This paper introduces a novel method to determine the failure time distribution functions using possibility theory. For this purpose, fuzzy‐bathtub distributions using expert opinions are generated for basic events and fuzzy formulas are derived for static and dynamic gates fault tree constructions. This process completed by proposed fuzzy Monte Carlo simulation throughout the preferred operational time and uses the actual time‐to‐failure data. Accordingly, the Top Event failure curve and the reliability profile of the system are depicted based on the defuzzificated basic‐events' bathtub‐failure‐rates. The results show that the proposed method not only is feasible and powerful but can also be accurate more than the other probabilistic and possibilistic techniques because of the component failure rates follow the real failure distributions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the notion of isoclinism on a pair of n-Lie algebras, which forms an equivalence relation. In addition, we prove that each equivalence class contains a stem pair of n-Lie algebras, which has minimal dimension amongst the finite dimensional pairs of n-Lie algebras. Finally, some more results are obtained when two isoclinic pairs of n-Lie algebras are given. [ABSTRACT FROM AUTHOR]

The third author et al. in 2013, introduced and studied the concept of auto-Bell groups. A group G is said to be n-auto-Bell if [xn, α] = [x, αn], for all x in G, α in Aut(G) and any integer n ≠ 0, 1. Let Ln(G) be the nth-absolute centre of the group G, then some sharp bounds for the exponents of G/L2(G) and G/L3 (G) are constructed, when G is an n-auto-Bell abelian or n-auto-Bell groups. Finally, we show that <øx, α> is nilpotent of class at most 4, for every inner automorphism øx induced by an element x of G and α in Aut(G), when G is a 3-auto-Engel group. [ABSTRACT FROM AUTHOR]