Delays In State Variables Research Articles

Combining Augmented Error Modeling Technique and Block-Pulse Functions Method for Tracking Control Design of Nonlinear Polynomial Systems with Multiple Time-Delayed States Subject to Nonsymmetric Input Saturation

The present research work is intended to synthesize a novel tracking control strategy for a class of nonlinear polynomial systems characterized by multiple well-defined delays in state variables under the presence of nonsymmetric input saturation. The design strategy makes full use of an associate’s memory nonlinear state feedback control with integral-based actions. An original control scheme joining block-pulse functions method combined with the augmented error modeling technique is used to infer the controller’s tracking gains. The objective is to convert the investigated nonlinear algebraic problem governed by specifying constraints into a constrained linear one that can be solved in the constrained least square methodology. Detailed novel sufficient conditions proving the closed-loop augmented system’s practical stability are elaborated. The instance of a twofold inverted pendulums benchmark is considered so as to exhibit the benefits of the proposed control approach.

Quantification of Flexibility of a District Heating System for the Power Grid

District heating systems (DHS) that generate/consume electricity are increasingly used to provide flexibility to power grids. The quantification of flexibility from a DHS is challenging due to its complex thermal dynamics and time-delay effects. This article proposes a three-stage methodology to quantify the maximum flexibility of a DHS. The DHS is firstly decomposed into multiple parallel subsystems with simpler topological structures. The maximum flexibility of each subsystem is then formulated as an optimal control problem with time delays in state variables. Finally, the available flexibility from the original DHS is estimated by aggregating the flexibility of all subsystems. Numerical results reveal that a DHS with longer pipelines has more flexibility but using this flexibility may lead to extra actions in equipment such as the opening position adjustment of valves, in order to restore the DHS to normal states after providing flexibility. Impacts of the supply temperature of the heat producer, the heat loss coefficient of buildings and the ambient temperature on the available flexibility were quantified.

Controllability of Nonlinear Fractional Delay Dynamical Systems

This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag—Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.

Multirate output sampling linear functional observer-based state feedback for systems with delay in state variables

In this paper the design of functional observer-based state feedback controller for linear time-invariant (LTI) systems with time-delay in state variables is addressed. To illustrate the approach we consider a dual-rate system with fast output measurements and slow control actions. Necessary and sufficient conditions are given for existence of proposed controller with minimal number of output samples than those already employed multirate output sampling (MROS) and full state observability is not a necessary condition. By the so-called lifting method, time-delay systems are transformed into delay-free systems such that simple conditions have been developed for the stability and stabilisation. Design example is given to illustrate the procedure for the design of proposed controller and to demonstrate the advantages.

Robust Mixed$H_2/H_infty$Filtering for Time-Delay Fuzzy Systems

In this paper, a robust mixed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_2/H_infty$</tex> filtering problem for continuous-time fuzzy systems subject to parameter uncertainties and multiple time-varying delays in state variables is addressed. The uncertain systems are expressed as Takagi–Sugeno fuzzy models with linear nominal parts and norm-bounded uncertainties. The main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_infty$</tex> performance under worst case disturbance. Based on Lyapunov theory, both delay-independent and delay-dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities. Therefore, stable filters can be obtained easily with existing convex algorithms. Lastly, two examples are given to illustrate the proposed design methodology.

Robust mixed H 2/H ∞ filtering for discrete-time delay fuzzy systems

A robust mixed H 2/H∞ filtering problem for discrete-time fuzzy systems subject to parameter uncertainties and multiple time-varying delays in state variables is addressed in this paper. The uncertain systems are expressed as Takagi-Sugeno fuzzy models with linear nominal parts and norm-bounded uncertainties. The main objective is to design a stable filter which minimizes a guaranteed cost index and achieves a prescribed H∞ performance under worst-case disturbance. Based on Lyapunov theory, sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of LMIs. Therefore, stable filters are obtained with existing convex algorithms. Lastly, two examples are given to illustrate the proposed design methodology.

Linear functional observers for systems with delays in State variables: the discrete-time case

This note extends to the discrete-time case the design of linear functional state observers, recently developed for continuous-time delay systems. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear and bilinear matrix inequalities [(LMIs) and (BMIs)] formulations.

652 非線形時間遅れ最小位相系の安定条件(振動応用と制御, OS-10 非線形力学と力学系理論)

In this paper nonlinear minimum phase systems with time delay in state variables are considered. Time delay is an applied problem. It is well known that some examples are given in biology chemistry, economics, mechanics, physics, physiology, population dynamics, as well as in engineering sciences. Stability theory on the time delay system, generally expressed as functional differential equation, is useful to address those problems. However stability theory of functional differential equation is immature, and further development is expected. In the case of nonlinear functional differential equation, effective analysis tools are limited to Lyapunov-Krasovskii pan-function and Lyapunov-Razumikhin function. Objective in this paper is to propose one of the stability distinctions toward nonlinear functional differential equation.

Controllability of nonstandard singularly perturbed systems with small state delay

A nonstandard singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two much simpler parameter-free systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. Due to the nonstandard nature of the original system, the reduced-order one is descriptor (differential-algebraic). A connection between the properties of controllability of these systems and such a property of the original system itself, robust in the small parameter of singular perturbations, is established. A criterion of the impulse-free controllability with respect to the slow variable of the reduced-order system is obtained, and the invariance of this criterion to an auxiliary gain matrix is shown.

Correction to "Linear functional observers for systems with delays in state variables"

Correction to "Linear functional observers for systems with delays in state variables"

Euclidean space controllability of singularly perturbed linear systems with state delay

A singularly perturbed linear time-dependent control system with small point and distributed delays in state variables is considered. Connections between the properties of controllability of the reduced-order and boundary-layer systems, associated with the original one, and such a property of the original system itself are established.

Linear functional observers for systems with delays in state variables

This paper is concerned with the design of linear functional state observers for systems with delays in state variables. In particular, the necessary and sufficient conditions for the existence of the rth-order observers are given. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix-in-equality formulation. A systematic design method of these observers is presented. Numerical examples are given to illustrate this method.

Controllability of singularly perturbed linear time-dependent systems with small state delay

A singularly perturbed linear time-dependent control system with multiple point and distributed small delays in state variables is considered. Two lower-dimension systems (the reduced-order and the boundary-layer ones), associated with the original system, are introduced. The reduced-order and the boundary-layer systems are in separate time scales, and they do not contain the small parameter any more. Connections between the properties of controllability of these systems and such a property of the original system itself are established for all sufficiently small values of the parameter of singular perturbations.

Asymptotic Solution of a Cheap Control Problem with State Delay

A linear-quadratic optimal control problem with point and distributed delays in state variables and a small control cost in the performance index is considered. An asymptotic solution of the singularly perturbed set of Riccati-type functional-differential equations, associated with this problem, is constructed and justified. Based on this solution, the suboptimal feedback control law is derived. An accuracy of the corresponding value of the performance index is established.

Input-output linearization of nonlinear systems with time delays in state variables

The present paper is concerned with nonlinear systems that contain delays inside coupled with a part of state variables, which are often the cases in practical problems, but have not been treated yet. First we introduce an extension of the Lie derivative for a difference-differential equation; then we derive necessary and sufficient conditions for existence of a nonlinear feedback that linearizes the input-output behaviour of a system and decouples it from the delayed variables simultaneously. Discussions are given for two cases: firstly when the linearizing feedback contains only current values of state variables, and secondly when the linearizing feedback has memories to utilize the past values as well as the current values of state variables.

An observer of systems with delays in state variables

The paper is concerned with the design of an observer of systems with delays in state variables and control. It is shown, on the basis of the finite spectrum assignment theory, that if the system is spectrally observable, there exists an observer which can estimate the state variables of the system as fast as desired. A systematic design procedure of the observer is presented. The advantage of the proposed method is that the observer is constructed without preliminary knowledge of the open-loop spectrum in contrast with the design method based on the spectral decomposition.

状態にむだ時間をもつ多変数系の有限極配置

状態にむだ時間をもつ多変数系の有限極配置

Further study of spectral controllability of systems with multiple commensurate delays in state variables

The paper presents a necessary and sufficient condition for spectral controllability of systems with multiple commensurate delays in state variables on the basis of finite Laplace transforms.

Finite spectrum assignment problem for systems with multiple commensurate delays in state variables

Abstract This paper is concerned with the finite spectrum assignment problem for systems with multiple commensurate delays in state variables. The necessary and sufficient condition for finite spectrum assignability is clarified. A systematic design procedure which can straightforwardly yield a control law is presented.

Finite spectrum assignment problem for systems with delay in state variables

This correspondence is concerned with the finite spectrum assignment problem for linear systems with delay in state variables. A systematic procedure for constructing the feedback law is presented on the basis of advanced elementary row operations on matrices with two variables s and z = e^{-sh} .