An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections

In this paper, the problem of distributed functional state observer design for a class of large-scale interconnected systems in the presence of heterogeneous time-varying delays in the interconnections and the local state vectors is considered. The resulting observer scheme is suitable for strongly coupled subsystems with multiple time-varying delays, and is shown to give better results for systems with very strong interconnections while only some mild existence conditions are imposed. A set of existence conditions are derived along with a computationally simple observer constructive procedure. Based on the Lyapunov-Krasovskii functional method (LKF) in the framework of linear matrix inequalities (LMIs), delay-dependent conditions are derived to obtain the observer parameters ensuring the exponential convergence of the observer error dynamics. The effectiveness of the obtained results is illustrated and tested through a numerical example of a three-area interconnected system.

Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

New finite-sum inequalities with applications to stability of discrete time-delay systems

This paper is concerned with the problem of stability analysis of discrete time-delay systems. New finite-sum inequalities, which encompass the ones based on Abel lemma or Wirtinger type inequality, are first proposed. The potential capability of the newly derived inequalities is then demonstrated by establishing less conservative stability conditions for some classes of linear discrete-time systems with delay. The derived stability criteria are theoretically and numerically proved to be less conservative than existing results.

Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances

This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.

Functional state observers design for interconnected time-delay systems

His research contributes to the field of functional state estimation for interconnected time-delay systems. Through progressive improvements and refinements, these developed observer structures have practical application for industry and more widely in the engineering field.

Partial state estimation of time-delay systems.

This thesis broadly studies three crucial and rigorous inter-related control theoretical subjects: (i) Partial state estimation of linear systems; (ii) Stability analysis of time-delay systems with interval time-varying delays; and (iii) Functional observer design for time-delay systems.

Design of reduced-order positive linear functional observers for positive time-delay systems

This brief considers a new problem of designing reduced-order positive linear functional observers for positive time-delay systems. The order of the designed functional observers is equal to the dimension of the functional state vector to be estimated. The designed functional observers always nonnegative at any time and they converge asymptotically to the true functional state vector. Moreover, conditions for the existence of such positive linear functional observers are formulated in terms of linear programming (LP). Numerical examples and simulation results are given to illustrate the effectiveness of the proposed design method.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.

Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

An improved stability criterion for time-delay power systems with electric vehicles and high voltage direct current power links

This paper presents an improved stability criterion for load frequency control (LFC) of time-delay power systems including AC/HVDC transmission links and EVs. By employing a novel refined Jensen-based inequality, an improved stability condition is derived in terms of feasible linear matrix inequalities (LMIs) which allow us to compute the maximal upper bounds of time-delay ensuring stability of the LFC scheme equipped with an embedded controller. Cases studies here are implemented for LFC scheme of a two-area power system, which is interconnected by parallel (AC/HVDC) links, with embedded proportional integral (PI) controller for discharged EVs. The relationships between the parameters of PI controller, supplementary control of HVDC links and delay margins of the LFC scheme are also discussed. As a consequence of facts, the results of delay margins can be used as a guideline to tune PI controller and set-up parameters for HVDC control.

Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control

In this paper, for the first time, electric vehicles are used for both the primary and secondary frequency controls to support power plants to rapidly suppress fluctuations in the system frequency due to load disturbances. Via networked control and wide-area communication infrastructures, multiple interval time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. By coordinating batteries’ state of charge control, the behaviors of the vehicle owners and the uncertainties imposed by the changes of the batteries’ state of charge are taken intoconsideration. A power system model incorporating multiple time-varying delays and uncertainties is first proposed. Then, a robust static output feedback frequency controller is designed to guarantee the resulting closed-loop system stable with an H∞ attenuation level. By utilizing a novel integral inequality, namely refined-Jensen inequality, and an improved reciprocally convex combination, the design conditions are formulated in terms of tractable linear matrix inequalities which can be efficiently solved by various computational tools. The effectiveness of the proposed control scheme is verified by extensive simulations.

Localization with ghost elimination of emitters via time-delay-of-arrival measurements

This paper investigates the theoretical requirements for unique localization of multiple emitters using time delay of arrival(TDoA) subjected to the data-association problem. Specifically, an examination is carried out to find the necessary fundamental requirements to solve the so-called ghost node problem pertaining to sensor arrays.

Exponential stabilization for state and input delay systems via output feedback

This paper considers the exponential stabilization problem via static and dynamic output feedback controllers of linear systems with a time delay in both the state and input. By using a change of the state variable and combining with the Lyapunov-Krasovskii method, new sufficient conditions for exponential stabilization via static and dynamic output feedback controllers are proposed. The conditions are expressed in terms of matrix inequalities but with only one parameter needs to be tuned and therefore can be efficiently solved by incorporating an one-dimensional search method into the Matlab’s LMI toolbox. Two numerical examples are provided to illustrate the obtained results.