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: This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.
Abstract: In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
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: In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.
Abstract: In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.
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: ELS is an important ground based hardware in the
loop simulator used for aerodynamics torque loading experiments
of the actuators under test. This work focuses on improvement of the
transient response of torque controller with parameters uncertainty
of Electrical Load Simulator (ELS).The parameters of load simulator
are estimated online and the model is updated, eliminating the model
error and improving the steady state torque tracking response of
torque controller. To improve the Transient control performance the
gain of robust term of SMC is updated online using fuzzy logic
system based on the amount of uncertainty in parameters of load
simulator. The states of load simulator which cannot be measured
directly are estimated using luenberger observer with update of new
estimated parameters. The stability of the control scheme is verified
using Lyapunov theorem. The validity of proposed control scheme is
verified using simulations.
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 aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.
Abstract: This paper considers the autonomous navigation
problem of multiple n-link nonholonomic mobile manipulators within
an obstacle-ridden environment. We present a set of nonlinear
acceleration controllers, derived from the Lyapunov-based control
scheme, which generates collision-free trajectories of the mobile
manipulators from initial configurations to final configurations in a
constrained environment cluttered with stationary solid objects of
different shapes and sizes. We demonstrate the efficiency of the
control scheme and the resulting acceleration controllers of the
mobile manipulators with results through computer simulations of an
interesting scenario.
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: This paper is concerned with the delay-distributiondependent
stability criteria for bidirectional associative memory
(BAM) neural networks with time-varying delays. Based on the
Lyapunov-Krasovskii functional and stochastic analysis approach,
a delay-probability-distribution-dependent sufficient condition is derived
to achieve the globally asymptotically mean square stable of
the considered BAM neural networks. The criteria are formulated in
terms of a set of linear matrix inequalities (LMIs), which can be
checked efficiently by use of some standard numerical packages. Finally,
a numerical example and its simulation is given to demonstrate
the usefulness and effectiveness of the proposed results.
Abstract: Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.
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.