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Guaranteed cost finite-time control of positive switched nonlinear systems withD-perturbation

100%
Xing H., Liu L., Cao X., Fu Z., Song S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1635-1648
EN
This paper considers the guaranteed cost finite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and sufficient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the effectiveness of the proposed method.
2
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Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems

100%
Li Q., Liu S.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1035-1047
EN
In this paper, for multiple different chaotic systems with unknown bounded disturbances and fully unknown parameters, a more general synchronization method called modified function projective multi-lag combined synchronization is proposed. This new method covers almost all of the synchronization methods available. As an advantage of the new method, the drive system is a linear combination of multiple chaotic systems, which makes the signal hidden channels more abundant and the signal hidden methods more flexible. Based on the finite-time stability theory and the sliding mode variable structure control technique, a dual-stage adaptive variable structure control scheme is established to realize the finite-time synchronization and to tackle the parameters well. The detailed theoretical derivation and representative numerical simulation is put forward to demonstrate the correctness and effectiveness of the advanced scheme.
3
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Controllability of the Strongly Damped Wave Equation with Impulses and Delay

81%
Leiva H.
Nonautonomous Dynamical Systems
|
2017
|
tom 4
|
nr 1
31-39
EN
Evading fixed point theorems we prove the interior approximate controllability of the following semilinear strongly damped wave equation with impulses and delay [...] in the space Z1/2 = D((−Δ)1/2)×L2(Ω),where r > 0 is the delay, Γ = (0, τ)×Ω, ∂Γ = (0, τ) × ∂Ω, Γr = [−r, 0] × Ω, (ϕ,ψ) ∈ C([−r, 0]; Z1/2), k = 1, 2, . . . , p, Ω is a bounded domain in ℝℕ(ℕ ≥ 1), ω is an open nonempty subset of , 1 ω denotes the characteristic function of the set ω, the distributed control u ∈ L2(0, τ; U), with U = L2(Ω),η,γ, are positive numbers and f , Ik ∈ C([0, τ] × ℝ × ℝ; ℝ), k = 1, 2, 3, . . . , p. Under some conditions we prove the following statement: For all open nonempty subsets Ω of the system is approximately controllable on [0,τ]. Moreover, we exhibit a sequence of controls steering the nonlinear system from an initial state (ϕ (0), ψ(0)) to an ε-neighborhood of the final state z1 at time τ > 0.
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