Sensor fault diagnosis of time-delay systems based on adaptive observer

Presents a novel approach for the sensor fault diagnosis of time-delay systems by using an adaptive observer technique. The sensor tault is modeled as an additive perturbation described by a time varying function. Systems without model uncertainty are initially considered, followed by a discussion of a general situation where the system is subjected to either model uncertainty or external disturbance. An adaptive diagnostic algorithm is developed to diagnose the fault, and a modified version is proposed for general system to improve robusiness. The stability of fault diagnosis system is proved. Finally, a numerical example is given to illustrate the efficiency of the proposed method.

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.

Stabilization of the Cascaded ODE-Schrödinger Equations Subject to Observation With Time Delay

This paper focuses on the stabilization of the cascaded Schrodinger-ODE equations subject to the observation with time delay.Both observer and predictor systems are designed to estimate the state variable on the time interval[0,t-τ]when the observation is available,and to predict the state variable on the time interval[t-τ,t]when the observation is not available,respectively.Based on the estimated state variable and the output feedback stabilizing controller using the backstepping method,it is shown that the closed-loop system is exponentially stable.

Robust fault diagnosis for linear time-delay systems with uncertainty

This paper deals with the problem of fault diagnosis problem for a class of linear systems with delayed state and uncertainty. The systems are transformed into two different subsystems. One is not affected by actuator faults so that a robust observer can be designed under certain conditions. The other whose states can be measured is affected by the faults. The proposed observer is utilized in an analytical-redundancy-based approach for actuator and sensor fault detection and diagnosis in time-delay systems. Finally, the applicability and effectiveness of the proposed method is illustrated through numerical examples.

Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

ROBUST STABILITY CRITERIA FOR SYSTEM WITH DELAY & ITS APPLICATION TO FCS

A study is devoted to the delay robust stability for linear system with time delay, using matrix analysis and comparison theory on differential integral difference equations. Since the matrix norm used to derive the results may be arbitrary consistent matrix norm, the obtained results possess some agility, and it makes quite convenient to check stability for linear systems with time delay. In particular, a sufficient and necessary condition for delay robust stability is obtained, and a formula to calculate the maximum delay for systems with stability is given. At the end, the results are used to analyze a flight control system (FCS). Comparison with some literature shows that the criteria in this paper are not only simple, but also of small conservativeness.

Convergence, stability and robustness analysis of the OFEX controller for high-speed networks

The OFEX （Optimal and Fully EXplicit） rate controller is able to provide not only the optimal bandwidth allocation but also the fully explicit congestion signal to sources. It exercises link-wise proportional fairness and network-wise max-min fairness, which enables the controller to feed the congestion signal back from the most congested link, instead of using the network- wise proportional fairness which feeds back the congestion signal summed along a flow path. As a result, the OFEX controller overcomes the drawbacks of the relatively explicit controllers that 1） bias the multi-bottlenecked users in terms of their source sending rate and convergence speed, 2） are not adaptable to varying link bandwidth and 3） can potentially incur large queue size upon congestion. In this paper, we first prove that the OFEX controller can converge to its equilibrium at least as fast as a geometric series in a link. Then we analyze the system stability with time delay in a single bottleneck network and show that the OFEX controller can achieve local stability under certain conditions. Besides, the robustness analysis of the OFEX controller shows how the dynamics of link bandwidth may affect the revenue of a link. Finally, with the OPNET modeler, we evaluate the performances of the OFEX controller and verify its effectiveness.

Design of decoupling Smith control for multivariable system with time delays

In order to solve the decoupling control problem of multivariable system with time delays,a new decoupling Smith control method for multivariable system with time delays was proposed. Firstly,the decoupler based on the adjoint matrix of the multivariable system model with time delays was introduced,and the decoupled models were reduced to first-order plus time delay models by analyzing the amplitude-frequency and phase-frequency characteristics. Secondly,according to the closed-loop characteristic equation of Smith predictor structure,proportion integration (PI) controllers were designed following the principle of pole assignment for Butterworth filter. Finally,using small-gain theorem and Nyquist stability criterion,sufficient and necessary conditions for robust stability were analyzed with multiplicative uncertainties,which could be encountered frequently in practice. The result shows that the method proposed has superiority for response speed and load disturbance rejection performance.

Robust Stability and Performance Comparison of PID and PPI Control

Predictive PI (PPI) control form, capable of time delay compensation, has been put forward recently. This control algorithm is essentially a PI controller with enhanced derivative action, which is not only suitable for long time delay process, but also of simple structure and excellent robust stability. The performance of PPI controller was demonstrated and compared with that of traditional PID controller by different tuning methods.

Robust Stability Analysis of a Kind of Combined Integrating Control System

This paper offeres an exact study on the robust stability of a kind of combined integrating control system, and the robust stability belongs to the analysis of a kind of quasi-polynomial with two independent time delays. The parameters of stable space under time delay uncertainty are fixed after Rekasius transformation, and then a new cluster treatment of characteristic roots (CTCR) procedure is adopted to determine the stable space. By this strategy we find that the unstable space is not continuous and both Karitonov vertices theory and Edge theory are unable to be extended to quasi-polynomial under time delay uncertainty.

Stabilizing Hybrid Stochastic Interval Systems by Feedback Controls

The problem of stabilizing a hybrid stochastic interval system is studied in this article. A hybrid interval system with suitable controls will become stable in the sense of mean-square exponential stability. State-feedback controls are designed based on the discrete-time state observations. Controls are put both in the drift and diffusion parts of the system. Criteria are derived in terms of linear matrix inequalities( LMI) to get the controllers. Also one example is given to illustrate our techniques.

Observer-based Adaptive Fuzzy Control for a Class of Nonlinear Time-delay Systems

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Robust stability analysis of switched uncertain systems with multiple time-varying delays and actuator failures

In this paper,the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered.Based on the average dwell time approach,a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one.It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under these switching laws.Particularly,the maximal upper bound of delays can be obtained from the linear matrix inequalities.At last,the effectiveness of the proposed method is demonstrated by a simulation example.

ON GLOBAL ROBUST STABILITY FOR COMPETITIVE NEURAL NETWORKS WITH TIME DELAYS AND DIFFERENT TIME SCALES

In this paper, using the theory of topological degree and Liapunov functional methods, the authors study the competitive neural networks with time delays and different time scales and present some criteria of global robust stability for this neural network model.

Output Feedback Stabilization of an Unstable Wave Equation with Observations Subject to Time Delay

This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed:The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.

Robust Stabilization of Uncertain Time Delay System

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Robustness analysis and distributed control of a networked system with time-varying delays

This paper is concerned with the robustness analysis and distributed output feedback control of a networked system with uncertain time-varying communication delays.This system consists of a collection of linear time-invariant subsystems that are spatially interconnected via an arbitrary directed network.Using a dissipation inequality that incorporates dynamic hard lQCs(integral quadratic constraints)for the delay uncertainties,we derive some sufficient robustness conditions in the form of coupled linear matrix inequalities,in which the couplld parts reflect the interconnection structure of the system.We then provide a procedure to construct a distributed controller to ensure the robust stability of the closed-loop system and to achieve a prescribed lzgain performance.The effectiveness of the proposed approach is demonstrated by some numerical examples.

Robust stabilization of stochastic differential inclusion systems with time delay

This paper is concerned with robust stabilization of stochastic differential inclusion systems with time delay. A nonlinear feedback law is established by using convex hull quadratic Lyapunov function such that the closed-loop system is exponentially stable in mean square. Sufficient conditions for the existence of the feedback are obtained via linear matrix inequalities （LMIs）. An example is given to illustrate the effectiveness of the proposed method.

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.

The Effect of Small Time Delays in the Feedbacks on Boundary Stabilization~*

In this paper we discuss the effect of small time delays in the feedbacks on stabilization. It is proved that with respect to small time delays in the feedbacks, (boundary) stabilizations of parabolic systems are robust, but symmetric stabilization of intinitely-dimensional conservative systems is not robust. For example, the current boundary stabilization of the wave equation is not robust with respect to small time delays in its feedback. This is an answer to a problem posed in [1].