A New Sliding Function for Discrete Predictive Sliding Mode Control of Time Delay Systems

The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.

Delay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators

This note concerns the problem of the robust stability of uncertain neutral systems with time-varying delay and saturating actuators. The system considered is continuous in time with norm bounded parametric uncertainties. By incorporating the free weighing matrix approach developed recently, some new delay-dependent stability conditions in terms of linear matrix inequalities （LMIs） with some tuning parameters are obtained. An estimate of the domain of attraction of the closed-loop system under a priori designed controller is proposed. The approach is based on a polytopic description of the actuator saturation nonlinearities and the Lyapunov- Krasovskii method. Numerical examples are used to demonstrate the effectiveness of the proposed design method.

Stabilization of a class of nonlinear discrete time systems with time varying delay

The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.

Online Delay-Evaluation Control for Networked Control Systems

This paper presented an evaluation approach of time delays for networked control systems (NCS). An improved scheme based on optimal LQG control was designed to achieve desired performance despite the uncertain delays in the system. The experimental results illustrate the effectiveness of the proposed control design and satisfactory performance of the closed loop system.

Advanced Identification Methods for Industrial Processes with Big Time Delays

This paper presents an advanced method for system identification of industrial processes with big time delays. Identification methods based on neural networks, tree partitioning and wavelet networks are presented and analyzed. The obtained results are compared and the tree partitioning method is selected as most appropriate identification method for the water treatment process. The decision was made based on a thorough analysis on the overall fit between the measured data and the results of the simulated model. At the end, we propose possibilities for further research in this area.

Identification of integrating and critically damped systems with time delay

This paper presents identification of second order plus dead time （SOPDT） integrating and critically damped systems based on relay feedback testing. Relay with hysteresis is applied to the unknown system to get the sustained oscillations also called as limit cycle. The limit cycle parameters are utilized in mathematical expressions which are derived using state space technique so that exact process model parameters are estimated. As the relay with hysteresis helps in generating sustained oscillations and also reduces effect of measurement noise which is an important issue in system identification. Different types of processes in the form of transfer function models are considered to show the efficacy of the proposed method and results are compared with available methods in the literature with and without noise effect.

Multivariable Fuzzy Predictive Control Based on the Modified CPN Model

Through modifying the CPN model, a kind of multivariable fuzzy model is put forward, and the matching fuzzy multistep predictive control algorithm is deduced based on the model. The modified model works in a competitive output manner which results in its local representation property. While studying on line, only a few parameters need to be regulated. So the model has the merits of fast learning and on line self organizing modeling. The control algorithm is simple, adaptive and useful in multivariable and time delay systems. Applying the algorithm in a paper making system, simulation shows its good effect.

Stability of Time-varying Linear Systems with Time Delays

Easy ways to test the stability of systems involving time delays have been sought.In this paper,some unconditional stability and asymptotically stable with decay rate α criteria for time-varying linear systems with time delays are presented by matrix measure and comparisontheorem.

Delay-dependent Robust Stability Analysis of Power Systems with PID Controller

This study examines the robust stability of a power system,which is based on proportional-integral-derivative load frequency control and involves uncertain parameters and time delays.The model of the system is firstly established,following which the system is transformed into a closed-loop system with feedback control.On this basis,a new augmented Lyapunov-Krasovskii(LK)functional is established for using the new Bessel-Legendre inequality to estimate the derivative of the functional,which can provide a maximum lower bound.A stability criterion is then derived by employing the LK functional and Bessel-Legendre inequality.Finally,numerical examples are used to demonstrate the validity and superiority of the proposed method.

Reduced-order functional observers with application to partial state estimation of linear systems with input-delays

Reduced-order multi-functional observer design for multi-input multi-output linear timeinvariant(LTI)systems with constant delayed-inputs is studied.This research is useful in the input estimation of LTI systems with actuator delay,as well as system monitoring and fault detection of these systems.Two approaches for designing an asymptotically stable functional observer for the system are proposed:delay-dependent and delay-free.The delay-dependent observer is infinite-dimensional,while the delay-free structure is finite-dimensional.Moreover,since the delay-free observer does not require any information on the time delay,it is more practical in real applications.However,the delay-dependent observer contains less restrictive assumptions and covers more variety of systems.The proposed observer design schemes are novel,simple to implement,and have improved numerical features compared to some of the other available approaches to design(unknown-input)functional observers.In addition,the proposed observers usually possess lower order than ordinary Luenberger observers,and the design schemes do not need the observability or detectability requirements of the system.The necessary and sufficient conditions of the existence of an asymptotic observer in each scenario are explored.The extensions of the proposed observers to systemswith multiple delayed-inputs are also discussed.Several numerical examples and simulation results are employed to support our theories.

Consensus on Intervals of Communication Delay

This paper brings out a structured methodology for identifying intervals of communication time-delay where consensus in directed networks of multiple agents with high-order integrator dynamics is achieved. It is built upon the stability analysis of a transformed consensus problem which preserves all the nonzero eigenvalues of the Laplacian matrix of the associated communication topology graph. It is shown that networks of agents with first-order integrator dynamics can be brought to consensus independently of communication delay, on the other hand, for agents with second-order integrator dynamics, the consensus is achieved independently of communication delay only if certain conditions axe satisfied. Conversely, if such conditions axe not satisfied, it is shown how to compute the intervals of communication delay where multiple agents with second-order or higher-order can be brought to consensus. The paper is ended by showing an interesting example of a network of agents with second-order integrator dynamics which is consensable on the first time-delay interval, but as the time-delay increases, it loses consensability on the second time-delay interval, then it becomes consensable again on the third time-delay interval, and finally it does not achieve consensus any more on the fourth time-delay interval. This example shows the importance of analyzing consensus with time-delay in different intervals.