Robust control problem of nonlinear time-delay chaotic systems is investigated. For such uncertain systems, we propose adaptive feedback controller and novel nonlinear feedback controller. They are both independent of the time delay and can render the corresponding closed-loop systems globally uniformly ultimately bounded stable. The simulations on controlling logistic system are made and the results show the controllers are feasible.

Robust stochastic stabilization and guaranteed cost control for a class of uncertain discrete-time linear system with Markovian jumping parameters are discussed. Two classes of controller gain perturbations, additive and multiplicative, are considered. The necessary and sufficient conditions for the above problems are derived, which are in terms of positive-definite solutions of a set of coupled linear matrix inequalities (LMIs). Furthermore, resilient guaranteed cost controllers are designed. Finally, numerical examples are presented to illustrate the solvability and effectiveness of the results.

This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable fixed point and to tracking an unstable periodic orbit, respectively. Some numerical examples are provided to demonstrate the effectiveness of the presented method.

This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.

The guaranteed cost control problem is studied for a class of 2D discrete uncertain systems in the Fornasini-Marchesini state space setting. The uncertainty is assumed to be norm bounded. Based on the guaranteed cost controller for 1D differential/difference systems, the notion of the guaranteed cost control problem for 2D discrete systems is proposed. The problem is to design both a static-state feedback controller and a dynamic output feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach. A parametrised characterisation of the guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Furthermore, a convex optimisation problem is formulated to select the optimal guaranteed cost controller which minimises the upper bound of the closed-loop cost function.

In this letter, we investigate the local stability in equilibrium for Internet congestion control algorithm proposed by Low (IEEE/ACMTRANSACTIONS ONNETWORKING, 1999). The network consists of multisource and one-bottleneck link with heterogenous time-varying propagation delays. Linear matrix inequality (LMI) stability criteria is presented for discrete congestion control algorithm of TCP/REM dual model, which can be efficiently and easily solved by the LMI toolbox provided by Matlab software. An important feature is to acquire the maximum network delays to guarantee the stability of congestion control algorithm, i.e., the scale stability domain of REM algorithm. Index Terms-Congestion control, linear matrix inequality (LMI), Local stability, REM.

This paper discusses an adaptive fuzzy controller design method for chaotic systems in the presence of completely unknown nonlinearities and disturbances. All the unknown nonlinear functions are estimated by dynamic fuzzy approximators so that the adaptive fuzzy control approach can be employed in the chaotic systems. Moreover, H∞ control method is applied to attenuate the effect of the modeling errors and disturbances in tracking control. An example is given to illustrate the effectiveness of this approach.

Control problem of chaotic system is investigated via adaptive method. A fairly simple adaptive controller is constructed, which can control chaotic systems to unstable fixed points. The precise mathematical models of chaotic systems need not be known and only the fixed points and the dimensions of chaotic systems are required to be known. Simulations on controlling different chaotic systems are investigated and the results show the validity and feasibility of the proposed controller.

In this note, the problem of control for a class of chaotic systems is studied. Only partial information of the systems states is known. First, an adaptive observer is designed to ensure the corresponding error system asymptotically stable. Then, based on the states obtained by the above observer, a nonlinear state feedback controller is constructed for the chaotic system, which, according to the input to state stable (ISS) principal, guarantees the closed-loop chaotic system is asymptotically stable. A numerical example is included to show the effectiveness of the proposed techniques.