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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]