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Summary This paper deals with the problem of delay-dependent H∞ exponential stability for neutral Markovian jump systems with mixed delays and nonlinear perturbations. Based on Lyapunov stability theory and linear matrix inequality method, some new H∞ exponential stability criteria are presented. The difference between this paper and other existing results is that the lower bounds of the neutral delay, the upper bounds of the neutral delay and discrete delay are considered, which will obtain some less conservative stability analysis results. Numerical examples are given to show that the proposed criteria improve the existing results.

Summary This paper investigates the problem of delay-dependent robust stochastic stabilization and H∞ control for uncertain stochastic nonlinear systems with time-varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H∞ control for uncertain stochastic system with time-varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed-loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.

Summary This paper deals with the fault detection and isolation (FDI) problem for uncertain closed-loop systems with external disturbances and nonlinear perturbations. To address the system uncertainties and the nonlinear perturbations in different faulty models, adaptive and switching techniques are introduced to construct a bank of FDI observers, such that one of them can match the current system, and the corresponding observer estimate errors can converge asymptotically to zero. An effective FDI scheme is then presented by introducing some model-matching indexes. Moreover, the introduced switching laws liberate the equality constraints often used in the existing FDI approaches, which are hard to satisfy if the system matrices include uncertainties. Finally, a simulation example of F/A-18A automatic carrier landing system is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper we study the existence of solutions for fractional Schrodinger equations of the form where V is a potential bounded and the nonlinear term has the critical exponential growth. We prove the existence of at least one weak solution by combining the mountain-pass theorem with the Trudinger–Moser inequality and a version of a result due to Lions for critical growth in .

Summary This paper addresses the stabilization problem of neutral systems. The neutral systems assumed to be subjected to nonlinear perturbations and mixed time-varying delays. Specifically, the adaptive control method is used to stabilize the unknown neutral systems. If the system states and the delayed states with its derivatives are available for measurement, a new and less conservative adaptive control algorithm is proposed, and sufficient conditions for the existence of the adaptive control are derived based on Lyapunov's stability theory. The main idea is to make all the stability conditions of the system depend on desired arbitrary matrices, not on the given system matrices. This is accomplished by the adaptation process. Illustrative examples with numerical simulations are studied. The simulation results show the effectiveness of the proposed design methods. Copyright © 2015 John Wiley & Sons, Ltd.

We prove the existence of solution for a class of p(x)-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.

SUMMARY This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any , where is a pre-defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an e-independent condition in terms of LMI related to is derived via using an e-dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean-square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the problem of μ-stability of impulsive differential systems with unbounded time-varying delays and nonlinear perturbations. Some μ-stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using Lyapunov–Krasovski functional method. Those criteria are expressed in the form of linear matrix inequalities and they can easily be checked. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is concerned with the energy decay for a class of plate equations with memory and lower order perturbation of p-Laplacian type, with simply supported boundary condition, where Ω is a bounded domain of , g > 0 is a memory kernel that decays exponentially and f(u) is a nonlinear perturbation. This kind of problem without the memory term models elastoplastic flows. Copyright © 2012 John Wiley & Sons, Ltd.

This paper investigates the delay-dependent adaptive synchronization problem of the master and slave structure of linear systems with both constant neutral and time-varying discrete time-delays and nonlinear perturbations based on the Barbalat lemma and matching conditions. An adaption law which includes the master-slave parameters is obtained by using the Lyapunov functional method and inequality techniques to synchronize the master-slave systems without the knowledge of upper bounds of perturbation terms. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example has been given to show the effectiveness of the method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

SUMMARY This paper investigates the consensus problem of a multi-agent directed network with nonlinear perturbations (MNNP). Our main objective is to study how the nonlinear perturbations affect a consensus of a multi-agent network. Based on a reduced-order transformation, it is shown that an MNNP cannot reach a consensus under a hypothesis even though the discussed network has a spanning tree. The hypothesis shows a detailed relationship between the nonlinear perturbations and the structure of the multi-agent network. An impulsive approach is then introduced, and a simple criterion is presented to guarantee the consensus of all agents for an MNNP. Finally, a numerical example is provided to illustrate the effectiveness of the obtained criterion. Copyright © 2011 John Wiley & Sons, Ltd.

This paper is concerned with the problem of the robust stability for T–S fuzzy systems with interval time-varying delay and nonlinear perturbations. The key features of the approach include the introduction of uncorrelated augmented matrix items into the Lyapunov functional and the use of some appropriate integral inequalities. Unlike the existing methodologies, the proposed approach involves neither free weighting matrices nor any model transformation. It can, however, lead to much less conservative stability criteria than the existing ones for the systems under consideration. The cases of perturbations are assumed to both nonlinear time-varying perturbations and time-varying uncertainties in linear fractional form. Numerical examples show that the obtained results are less conservative than the existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

We consider spatiotemporal systems and study their l∞ and l2 robustness properties in the presence of spatiotemporal perturbations. In particular, we consider spatially invariant nominal models and provide necessary and sufficient conditions for system robustness for the cases when the underlying perturbations are linear spatiotemporal varying, and nonlinear spatiotemporal invariant, unstructured or structured. It turns out that these conditions are analogous to the scaled small gain condition (which is equivalent to a spectral radius condition and a linear matrix inequality for the l∞ and l2 cases, respectively) derived for standard linear time-invariant models subject to time-varying linear and time-invariant nonlinear perturbations. Copyright © 2009 John Wiley & Sons, Ltd.

The robust feedback stabilization of a class of nonlinear discrete-time systems with unknown constant state-delay and uncertain function of nonlinear perturbations is considered based on linear matrix inequality (LMI)-based analysis and design procedures. In both cases of nominal and resilient feedback designs, the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. A dynamic output feedback controller is then designed for this class of systems. Seeking computational convenience, all the developed results are cast in the format of LMIs and several numerical examples are presented throughout the paper to demonstrate the advantages of the design methods. Copyright © 2007 John Wiley & Sons, Ltd.

The stabilization problem for a class of infinite-dimensional discrete-time nonlinear systems is discussed. Under an appropiate growth condition on the nonlinear perturbation combined with the ‘freezing’ method to discrete-time systems on Banach spaces, we establish explicit conditions for global feedback exponential stabilizability, and these conditions are easy to construct and to verify. This approach will allow us to avoid the construction of Lyapunov's functions in some situations. Copyright © 2009 John Wiley & Sons, Ltd.