Abstract: In this paper, we shall present sufficient conditions
for the ψ-exponential stability of a class of nonlinear impulsive
differential equations. We use the Lyapunov method with functions
that are not necessarily differentiable. In the last section, we give
some examples to support our theoretical results.
Abstract: In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.
Abstract: In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.
Abstract: This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.
Abstract: In the closed quantum system, if the control system is
strongly regular and all other eigenstates are directly coupled to the
target state, the control system can be asymptotically stabilized at the
target eigenstate by the Lyapunov control based on the state error.
However, if the control system is not strongly regular or as long as
there is one eigenstate not directly coupled to the target state, the
situations will become complicated. In this paper, we propose an
implicit Lyapunov control method based on the state error to solve the
convergence problems for these two degenerate cases. And at the same
time, we expand the target state from the eigenstate to the arbitrary
pure state. Especially, the proposed method is also applicable in the
control system with multi-control Hamiltonians. On this basis, the
convergence of the control systems is analyzed using the LaSalle
invariance principle. Furthermore, the relation between the implicit
Lyapunov functions of the state distance and the state error is
investigated. Finally, numerical simulations are carried out to verify
the effectiveness of the proposed implicit Lyapunov control method.
The comparisons of the control effect using the implicit Lyapunov
control method based on the state distance with that of the state error
are given.
Abstract: The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
Abstract: In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.
Abstract: In this paper, the decomposition-aggregation method
is used to carry out connective stability criteria for general linear
composite system via aggregation. The large scale system is
decomposed into a number of subsystems. By associating directed
graphs with dynamic systems in an essential way, we define the
relation between system structure and stability in the sense of
Lyapunov. The stability criteria is then associated with the stability
and system matrices of subsystems as well as those interconnected
terms among subsystems using the concepts of vector differential
inequalities and vector Lyapunov functions. Then, we show that the
stability of each subsystem and stability of the aggregate model
imply connective stability of the overall system. An example is
reported, showing the efficiency of the proposed technique.
Abstract: By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.
Abstract: This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.
Abstract: This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.
Abstract: In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.
Abstract: In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.
Abstract: This paper presents a new sufficient condition for the
existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters
of the neural system independently of the delay parameters. The results are also compared with the previously reported results in
the literature.
Abstract: In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.
Abstract: In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.
Abstract: In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.
Abstract: In this paper, a fuzzy controller is designed for
stabilization of the Lorenz chaotic equations. A simple Mamdani
inference method is used for this purpose. This method is very simple
and applicable for complex chaotic systems and it can be
implemented easily. The stability of close loop system is investigated
by the Lyapunov stabilization criterion. A Lyapunov function is
introduced and the global stability is proven. Finally, the
effectiveness of this method is illustrated by simulation results and it
is shown that the performance of the system is improved.
Abstract: In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
Abstract: In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.