A New Robust Stabilization Analysis Result for Uncertain Systems with Time-Varying Delay

The robust stabilization problem for uncertain systems with time-varying delay has been discussed. A new sufficient criterion is obtained to guarantee the closed-loop system robust stabilizable. The controller gain matrix is included in a Hamiltonian matrix. The Hamiltonian matrix can be constructed by the boundedness of the uncertainties. Some examples are given to illustrate the feasibility of the criterion.

PASSIVE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY SYSTEMS

This paper focuses on the passive control for a class of linear time delay system with norm bounded time varying parameter uncertainties by using a linear matrix inequality (LMI) approach. A sufficient condition under which the uncertain time delay system is quadratically stable and strictly passive for all admissible uncertainties was derived. It is shown that the solvability of problem of the robust passive controller design is implied by the feasibility of a linear matrix inequality.

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.

Robust Stabilization of Delayed Systems with Rank-1 Type Uncertainties

This paper deals with the problem of robust stabilizationfor the systems with rank-1 type uncertainties and mul-tiple state delay.Firstly,a new delay-dependent crite-ria is presented for unforced normal delayed system to bestable.Based on the obtained criteria,a new LMI ap-proach is developed for robust stabilization of a class ofuncertain delay systems via linear memoryless state feed-back control law.The results depend on the size of thedelays and are given in terms of linear matrix inequali-ties.And so no tuning procedure for scalars and/or ma-trices is required and the results are less conservativethan those of delay-independent.Finally,an illustra-tive example is presented.

Adaptive Robust Control of Multi-Machine Power Systems with Control Time Delay

The adaptive H_∞ control problem of multi-machine power system in the case of disturbances and uncertain parameters is discussed,based on a Hamiltonian model.Considered the effect of time delay during control and transmission,a Hamilton model with control time delay is established.Lyapunov-Krasovskii function is selected,and a controller which makes the system asymptotically stable is got.The controller not only achieves the stability control for nonlinear systems with time delay,but also has the ability to suppress the external disturbances and adaptive ability to system parameter perturbation.The simulation results show the effect of the controller.

Containment Control for First-Order Multi-Agent Systems with Time-Varying Delays and Uncertain Topologies

Containment control of first-order multi-agent systems with uncertain topologies and communication timedelays is studied. Suppose system topologies are dynamically changed, a containment control algorithm with time-varying delays is presented. The stability of the control algorithm is studied under the assumption that communication topologies are jointly-connected, and constraint condition of distributed containment control for delayed multi-agent systems is derived with the aid of Lyapunov–Krasovskii function. Simulation results are provided to prove the correctness and effectiveness of the conclusion.

STABILITY OF SINGULAR UNCERTAIN DIFFERENTIAL SYSTEMS WITH MULTIPLE TIME-VARYING DELAYS

The stability of singular uncertain differential systems with multiple time-varying delays is discussed, and many results on this are obtained.

DELAY-DEPENDENT ROBUST STABILITY CRITERIA FOR UNCERTAIN SINGULAR NEUTRAL DIFFERENTIAL SYSTEMS WITH TIME-VARYING AND DISTRIBUTED DELAYS

The problem of delay-dependent robust stability for uncertain linear singular neutral systems with time-varying and distributed delays is investigated. The uncertainties under consideration are norm bounded,and possibly time varying. Some new stability criteria,which are simpler and less conservative than existing results,are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coeffcient matrix and formulated in...

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) and nonlinear adaptive techniques.Some numerical examples are presented to demonstrate the effectiveness of the derived controller.

Discrete Quasi-Sliding Mode Tracking Controller with Time Delay Technique

Robust discrete quasi-sliding mode tracking controller is developed with discrete reaching law for trajectory tracking in the presence of modeling uncertainty and unknown disturbance. The conventional prior knowledge of uncertainty upper bounds being replaced by an on-line estimation used in the controller to cancel the slowly varying uncertainties by the mechanism of time delay. This method reduces the feedback gain substantially and improves tracking accuracy. The system behavior in the vicinity of the sliding surface is examined for the existence and bandwidth of quasi-sliding mode. Simulation results show the effectiveness of the strategy.

Decentralised dynamic high-gain scaling-based output-feedback control of large-scale non-linear interconnected systems with delays

A general class of non-linear large-scale interconnected systems is considered,wherein each subsystem is comprised of a nominal part in a general strict-feedback-like structure and a set of appended dynamics.Parametric and functional uncertainties and time delays are allowed throughout the overall system structure including the nominal strictfeedback-like parts and appended dynamics of each subsystem as well as the non-linear subsystem interconnections.The controller design is based on the dual dynamic highgain scaling technique and provides a robust adaptive delay-independent globally stabilising decentralised output-feedback controller.The disturbance attenuation properties of the proposed output-feedback decentralised controller to an exogenous disturbance input are also analysed and specific conditions under which properties such as Input-toOutput-practical-Stability and asymptotic stabilisation are attained are also discussed.

GUARANTEED COST CONTROL OF CONTINUOUS-TIME UNCERTAIN SINGULAR SYSTEM WITH BOTH STATE AND INPUT DELAYS

The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.