Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

Actuator fault detection and estimation for the Lur’e differential inclusion system

This paper deals with actuator fault detection and estimation for the Lur’e differential inclusion system. An adaptive full-order observer is used to detect the occurrence of the actuator fault. Then, based on a reduced-order observer, an approach to estimate the actuator fault is presented. A simulation of rotor system is given to illustrate the effectiveness of the proposed 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.     

Synchronization of chaotic Lur’e systems with quantized sampled-data controller

In this paper, we consider the master–slave synchronization problem of chaotic Lur’e systems. It is assumed that only quantized sampled measurements are available for the controller. By modeling the synchronization error system as an input-delay system and constructing a new Lyapunov functional, a new sufficient condition and feedback controller design method for global exponential asymptotical synchronization of master and slave system are obtained. The proposed approach has taken the feature of sample-induced delay into consideration and simulation results show the less conservativeness.     

Torsion of rigid circular shaft of varying diameter embedded in an elastic half space

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples of torsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented. Project Supported by the National Science Foundation of China.     

The creeping motion of multiple spherical liquid drops

This paper deals with the drag factor of the multiple spherical liquid drops in the creeping motion by means of the Sampson singularities and collocation technique. The drag factors of the drops are calculated under distinct conditions: different number of liquid drops in the chain and different sphere spacing. From the results the influence of the viscosity ratio on the shielding effect and end effect are revealed. The convergence of the method is also studied in this paper.In this paper the collocation technique developed by Gluckman et al. in treating the rigid sphere case is applied to deal with the creeping motion of multiple spherical liquid drops which has improtant applications in bioengineering and chemical engineering. Writing the general solutions in inner and outer regions of the spheres and satisfying the kinematic and dynamic matching conditions at the collocation points on the interfaces, a set of linear algebraic equations is obtained to determine the unknown coefficients in the solutions. By means of any matrix inversion technique the approximate solutions are presented. In the first section of this paper the mathematic formulation of the problem is given and then in the second section the numerical results are introduced and analysed.     

Improved stability criteria for neutral type Lur’e systems with time-varying delays

In this letter, the problem of stability analysis for neutral type Lur’e systems with interval time-varying delays is considered. By introducing a novel Lyapunov–Krasovskii (L–K) functional and utilizing second order reciprocal convex combination technique and Finsler lemma, an improved delay-dependent stability criteria is derived in terms of linear matrix inequalities (LMIs). The information about the time-varying delays and their upper bounds are fully used in the L–K functional. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.