共查询到20条相似文献，搜索用时 31 毫秒
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Xiongping Dai Tingwen Huang Yu Huang Yi Luo Gang Wang Mingqing Xiao 《Journal of The Franklin Institute》2017,354(10):4126-4155
Given any finite family of real d-by-d nonsingular matrices by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system:
we study the chaotic dynamics of the state trajectory (xn(x0, σ))n ≥ 1 with initial state governed by a switching law . Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (xn(x0, σ))n ≥ 1 are extremely sensitive to the initial states . We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws. 相似文献
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Akbar Zada Bakht Zada Jinde Cao Tongxing Li 《Journal of The Franklin Institute》2017,354(14):6247-6257
Let {Πτ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λτ(n), where is an arbitrary switching signal. We prove that the family {Πτ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence is bounded. 相似文献
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Michael Gil’ 《Journal of The Franklin Institute》2018,355(10):4241-4247
We consider the function Lyapunov equation where A and C are given matrices, f(z) is a function holomorphic on a neighborhood of the spectrum σ(A) of A. For a solution X of that equation, norm estimates are established. By these estimates we investigate perturbations of a matrix A whose spectrum satisfies the condition . In the case with a positive integer ν we obtain conditions that provide localization of the spectrum of a perturbed matrix in a given angle. 相似文献
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Xingping Sheng 《Journal of The Franklin Institute》2018,355(10):4282-4297
The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations . It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X0 and Y0. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form . Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ1 and µ2. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps. 相似文献
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This paper studies the stability of linear continuous-time systems with time-varying delay by employing new Lyapunov–Krasovskii functionals. Based on the new Lyapunov–Krasovskii functionals, more relaxed stability criteria are obtained. Firstly, in order to coordinate with the use of the third-order Bessel-Legendre inequality, a proper quadratic functional is constructed. Secondly, two couples of integral terms and are involved in the integral functionals and respectively, so that the coupling information between them can be fully utilized. Finally, two commonly-used numerical examples are given to demonstrate the effectiveness of the proposed method. 相似文献
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Consider the continuous-time matrix Riccati operator Ricc. In this work, we consider the robustness of this operator to direct perturbations of the matrices (A, R, S) and, in particular, the flow robustness of the corresponding Riccati differential equation. For a given class of perturbation, we show that the corresponding differential equation is well defined in the sense it is bounded above and below, it has a well-defined fixed point, and it converges to this fixed point exponentially fast. Moreover, the flow of the perturbed Riccati flow is close to the nominal Riccati flow when the perturbation is small; i.e. we prove a continuity-type condition in the size of the perturbation. 相似文献
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Shen-Ping Xiao Hong-Hai Lian Kok Lay Teo Hong-Bing Zeng Xiao-Hu Zhang 《Journal of The Franklin Institute》2018,355(17):8857-8873
This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from to and from to . Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature. 相似文献
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In this paper, dissipative consensus problems are discussed for multi-agent networks. Firstly, sufficient conditions are proposed to ensure dissipative consensus for multi-agent networks with external disturbances. Then, by designing an integral-type sliding surface function, a controller is obtained and the corresponding sufficient conditions are given to guarantee dissipative consensus for multi-agent networks with external disturbances. Moreover, the sliding mode control law is formulated such that multi-agent networks drive onto the predefined surface in finite time. Finally, an example is given to illustrate the effectiveness of the obtained results. 相似文献
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In this paper, methods for improved design of digital tracking controller for a pilot-scale unmanned helicopter are considered. By discretizing the linearized helicopter model, the linear quadratic with integral (LQI) capability is investigated and applied in order to develop an efficient tracking system including a state-feedback plus integral action. The helicopter velocities are used to formulate a prescribed position reference tracking trajectory. When both process and measurement noises are present, a Kalman filter (KF) is combined with the LQI to form a linear quadratic Gaussian with integral (LQGI) tracking system. Simulation studies illuminate both the capability of the controller design and the accuracy of the estimator. Next, H2, and mixed controls are designed and the results between methods are produced and compared. 相似文献
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The dynamics of multi-DOF aerial manipulators is complex system evolving in non-Euclidean Lie group, making design and tuning of the control of such systems challenge. In this paper we consider the nonlinear geometric control for aerial manipulation system. The linearized tracking error kinematic equation of motion on SO(3) is obtained from the variation on SO(3). Based on the linearized tracking error kinematic equation of motion on SO(3), the trajectory linearization control for the kinematics on SO(3) is investigated. The decoupled dynamics of multi-DOF aerial manipulator enables us to apply the results of trajectory linearization control for the kinematics on SO(3). We then design the entire controller for aerial manipulation system by composing different trajectory linearization control loops. Such controller structure eases the controller implementation and tuning procedure. The stability of the proposed controlled system is analyzed using Lyapunov’s method. The proof is finished from inner loop to outer loop. It is proven that the closed loop shape system is exponentially stable. The attraction basin of the configuration error for the shape system can almost cover the whole . The stability of the system considering the actuator dynamics and perturbations is also discussed in this paper. From the stability of the shape system, the stability of the entire system is proven. The stability analysis results are further verified through several numerical simulations. 相似文献
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