Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays

In this paper, the robust H∞control problem for a class of stochastic systems with interval time-varying and distributed delays is discussed. The system under study involves parameter uncertainty, stochastic disturbance, interval time-varying,and distributed delay. The aim is to design a delay-dependent robust H∞control which ensures the robust asymptotic stability of the given system and to express it in the form of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results are also compared with the existing results to show its conservativeness.     

Robust H_∞ observer-based control for synchronization of a class of complex dynamical networks

This paper is concerned with the robust H∞ synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities (LMIs). The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Robust H_∞ control of uncertain systems with two additive time-varying delays

This paper is concerned with the problem of delay-dependent robust H∞control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov–Krasovskii functional(LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H∞stability criteria are derived in terms of linear matrix inequalities(LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable.Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.     

Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed H∞ and passive projective synchronization problem for fractional-order(FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.     

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.     

Robust H∞ observer-based of a class of complex control for synchronization dynamical networks

This paper is concerned with the robust Hoo synchronization problem for a class of complex dynamical networks by applying the observer-based control. The proposed feedback control scheme is developed to ensure the asymptotic stability of the augmented system, to reconstruct the non-measurable state variables of each node and to improve the H∞ performance related to the synchronization error and observation error despite the external disturbance. Based on the Lyapunov stability theory, a synchronization criterion is obtained under which the controlled network can be robustly stabilized onto a desired state with a guaranteed H∞ performance. The controller and the observer gains can be given by the feasible solutions of a set of linear matrix inequalities （LMIs）. The effectiveness of the proposed control scheme is demonstrated by a numerical example through simulation.     

Robust output feedback cruise control for high-speed train movement with uncertain parameters

In this paper,the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated.The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers,which is subject to rolling mechanical resistance,aerodynamic drag and wind gust.Based on Lyapunov’s stability theory,the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs),under which the high-speed train tracks the desired speed,the relative spring displacement between the two neighboring cars is stable at the equilibrium state,and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed.One numerical example is given to illustrate the effectiveness of the proposed methods.     

Disturbance rejection and H∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.     

随机扰动下一般混沌系统的H∞同步

本文对随机扰动下的一般混沌系统进行了H_∞控制同步研究,其中扰动是布朗运动随机过程.基于随机李雅普诺夫稳定性理论、线性矩阵不等式、It公式以及H_∞控制方法,通过设置控制器,从理论上提出了驱动系统和随机扰动下的响应系统的H_∞渐近同步的新标准,这些标准形式简单且易于用Matlab实现.最后的数值模拟表明提出的理论结果的正确性和有效性. 关键词： 随机扰动 H_∞同步')" href="#">H_∞同步 线性矩阵不等式 It公式     

Turing pattern selection in a reactionben diffusion epidemic modelast

We present Turing pattern selection in a reaction—diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication: on increasing the control parameter v, the sequence “H₀ hexagons → H₀-hexagon-stripe mixtures → stripes → H_π-hexagon-stripe mixtures → H_π hexagons” is observed. This may enrich the pattern dynamics in a diffusive epidemic model.     

UV-visible spectral study on the stability of lead phthalocyanine complexes

UV-visible electronic spectral study has been done on lead phthalocyanine (PbPc), lead tetranitro phthalocyanine (PbTNP) and lead tetraamino phthalocyanine (PbTAP) in dimethyl sulphoxide (DMSO) and H₂SO₄ media. Metal free phthalocyanine (H₂Pc) is insoluble in DMSO and soluble in conc. H₂SO₄. The study has been extended to H₂Pc to compare the stability of phthalocyanine structure with the PbPc complexes in H₂SO₄ medium. PbPc complexes are stable in DMSO, and all the complexes are more stable in 36 N H₂SO₄ than in 30 N and 28 N H₂SO₄ media. Further, complete demetallation and degradation of the phthalocyanine structure have been observed for all the PbPc complexes in 36 N H₂SO₄ medium within a week's time. The stability of these complexes is compared with H₂Pc in H₂SO₄ medium. The decomposition reactions in H₂SO₄ media for H₂Pc, PbPc, PbTNP and PbTAP are followed spectrophotometrically and rate constants were calculated. The decomposition reactions were found to follow the first-order kinetics with respect to the concentration of their respective phthalocyanine derivatives.     

Chemical stability study of Li2SO4 on the operation condition of a H2/O2 fuel cell

The chemical stability of Li₂SO₄ on the operation condition of a H₂/O₂ fuel cell has been investigated in this work. Thermodynamic calculation indicates Li₂SO₄ can react with H₂ at high temperature. The H₂/O₂ fuel cell using Li₂SO₄–α-Al₂O₃ as electrolyte exhibits good performance, but the stability of performance is not good. XRD analysis indicates that Li₂SO₄ reacts with H₂ at high temperature. Therefore, the Li₂SO₄-based proton conductors are not suitable for electrolytes for H₂/O₂ fuel cells.     

Structures and electronic properties of stoichiometric hydrogenated aluminum clusters

The lowest-energy geometries and electronic-structure properties have been obtained for Al_nH_n (n=1-10) clusters within the density-functional theory using the generalized gradient approximation for the exchange correlation potential. The resulting geometries show that the hydrogen atoms tend to occupy outside positions and no hollow positions are found. The subunit Al_n of Al_nH_n (n=1-5) have little distortion, in comparison with corresponding pure Al_n cluster, whereas the subunit Al_n have large distortion from n=6. The stability has been investigated by analyzing the binding energy per atom and the second difference in energy, indicating that Al₈H₈ exhibit higher stability than others. The bonding property has been analyzed by calculating the Mulliken charges and Al–H distances. The calculated energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO), the vertical ionization potential, and the vertical electron affinity also confirm that Al₈H₈ is a stable cluster. The density of states (DOS) shows that Al_nH_n exhibit changes from molecular-like (Al₁H₁) to band-like structure (Al₁₀H₁₀) as n increases.     

Robust H∞ control of active vehicle suspension under non-stationary running

Due to complexity of the controlled objects, the selection of control strategies and algorithms in vehicle control system designs is an important task. Moreover, the control problem of automobile active suspensions has been become one of the important relevant investigations due to the constrained peculiarity and parameter uncertainty of mathematical models. In this study, after establishing the non-stationary road surface excitation model, a study on the active suspension control for non-stationary running condition was conducted using robust H_∞ control and linear matrix inequality optimization. The dynamic equation of a two-degree-of-freedom quarter car model with parameter uncertainty was derived. The H_∞ state feedback control strategy with time-domain hard constraints was proposed, and then was used to design the active suspension control system of the quarter car model. Time-domain analysis and parameter robustness analysis were carried out to evaluate the proposed controller stability. Simulation results show that the proposed control strategy has high systemic stability on the condition of non-stationary running and parameter uncertainty (including suspension mass, suspension stiffness and tire stiffness). The proposed control strategy can achieve a promising improvement on ride comfort and satisfy the requirements of dynamic suspension deflection, dynamic tire loads and required control forces within given constraints, as well as non-stationary running condition.     

Effects of B and N dopings and H2O adsorption on structural stability and field emission properties of cone-capped carbon nanotubes

The effects of B and N dopings and H₂O adsorption on the structural stability and the field emission properties of cone-capped carbon nanotubes (CCCNTs) were investigated by using the density-functional theoretical calculation. The adsorption of H₂O can increase the structural stability and decrease the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO gap) of the CCCNTs. The strength of total electric field on the top of the H₂O-adsorbed CCCNTs is larger than that of the B-doped and the N-doped CCCNTs, electrons will be emitted primarily from the H₂O-adsorbed CCCNTs at the same applied voltage. Therefore, the H₂O adsorption can lower the threshold voltage for the CCCNTs. While the B and the N dopings produce opposite effects. The HOMO-LUMO gap of the N-doped CCCNTs is the widest among all the gaps of the CCCNTs.     

Pattern selection in a predation model with self and cross diffusion

In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator--prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ₁<μ≤μ₂, the steady state is the only stable solution of the model; for μ₂<μ≤μ₄, by increasing the control parameter μ, the sequence H_π-hexagons → H₀-hexagon-stripe mixtures rightarrow stripes → H_π-hexagon-stripe mixtures → H₀-hexagons is observed; for μ>μ₄, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator--prey model.