Delay-dependent Observer Research Articles

Sampled-Data Output Feedback Leader-Following Scaled Consensus for Uncertain Nonlinear Multiagent Systems With Communication Delays and Noises

Communication delays and noises are common in practical problems. When they exist in the nonlinear multiagent system, this article addresses the leader-following scaled consensus problem. In the concerned system, nonlinearities can contain uncertainty and essential time-varying characteristic, and the output information is only available at sampling instants. In this article, we propose a class of time-varying gains to design the delay-dependent observer and control protocol, where a newly defined variable is used to cope with unknown noises. Under the output feedback control protocol, followers can asymptotically track the leader by assigned ratios. Different from existing works, the sampling period, communication delays, and noises are not restricted to a fixed upper bound. Two simulation examples are eventually presented to show the effectiveness of the proposed control protocol. Some future works can extend to general nonlinear systems with communication noises, and different time-varying delays.

Functional observers design for nonlinear discrete-time systems with interval time-varying delays

This paper is concerned with the functional observer design for a class of Multi-Input Multi-Output discrete-time systems with mixed time-varying delays. Firstly, using the Lyapunov-Krasovskii functional approach, we design the parameters of the delay-dependent observer. We establish the sufficient conditions to guarantee the exponential stability of functional observer error system. In addition, for design purposes, delay-dependent sufficient conditions are proposed in terms of matrix inequalities to guarantee that the functional observer error system is exponentially stable. Secondly, we presented the sufficient conditions of the existence of internal-delay independent functional observer to ensure the estimated error system is asymptotically stable. Furthermore, some sufficient conditions are obtained to guarantee that the internal-delay independent functional observer error system is exponentially stable. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed method.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent, and 2 – internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen׳s inequality, and improved Park׳s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

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 time-invariant (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 systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust againstL2norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.