LP-based observer design for switched positive linear time-delay systems

Liu, Lijuan; Zhao, Xudong; Sun, Xi‐Ming; Zong, Guangdeng

doi:10.1177/0142331218801128

Cited by 18 publications

(12 citation statements)

References 40 publications

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“…where i is the iteration index and τ is the time delay. Remark 1: Delays are very common in industrial processes and chemical processes [38]. For example, the gas chromatograph is modeled by a simple first-order system with some delays in [39].…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

Wang

Song²,

Zeng

2019

IEEE Access

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In this paper, the problem of iterative learning control with time delay is studied for linear timeinvariant (LTI) systems in the frequency domain. In terms of the LTI systems, which are formulated as one type of open-loop stable and minimum-phase systems with relative degree equaling to one, three different learning control schemes are proposed, such that the convergence of the tracking error can be guaranteed. The first scheme using the D-type algorithm with prediction can achieve wide convergence range. The second scheme applies an algorithm named A-type, which decreases noise. The third scheme is an improvement of the second one, which is a new type (AP-type) combination of the A-type and P-type ones. Moreover, for the systems with open-loop instability, non-minimum phase, and relative degree non-one, the convergence of the tracking error can still be ensured. Finally, some simulation examples are given to show the effectiveness of the proposed three control algorithms. INDEX TERMS Iterative learning control, time delay, frequency domain, anticipatory learning control.

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Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

Wang

Song²,

Zeng

2019

IEEE Access

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“…A switched system consists of a set of continuous (or discrete) time subsystems and the switching strategy between the subsystems (Liberzon, 2003; Sun and Ge, 2005). In the past few decades, the switched systems have attracted extensive attention due to both theoretical and practical reasons (Echreshavi and Roosta, 2018; Jin et al, 2019; Liu et al, 2019a, 2019b; Luo et al, 2020; Xiang et al, 2018; Xue et al, 2020; Yang et al, 2020; Zhao et al, 2017). The switched system plays an important role in many applications, such as aerospace systems Lian et al (2017) and networked control systems Deaecto et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

Hua

Tian

2022

Transactions of the Institute of Measurement and Control

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This paper studies the stabilization problem of a class of continuous-time switched linear systems with state constraints under pre-specified dwell-time switchings. Such systems are defined on a closed hypercube as all state variables are constrained to the unit hypercube. The dwell time in this paper is an arbitrarily pre-specified rather than a calculated constant, which is independent of any parameters. First, a class of multiple time-varying Lyapunov functions is introduced to study the stability analysis, and sufficient conditions on stability of the studied switched systems without control input are derived in the framework of pre-specified dwell-time switchings. The distinguishing feature of the proposed Lyapunov functions is that this type of delicately constructed Lyapunov functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functions at switching times. Second in the same framework of the dwell time, sufficient conditions for stabilization are proposed for that of the switched systems with state constraints by further designing state feedback controllers. Finally, two examples are provided to demonstrate the effectiveness of the proposed results. The results of this paper do not require to calculate the total time of each subsystem during which the state is saturated or non-saturated separately, which makes the pre-specified dwell-time switchings easy to apply.

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“…Moreover, there are also other researches in [22]- [25]. However, there still exits some problems to be solved, especially in observer design [26]- [30]. In recent, the LMIs approach has commonly used in observer design.…”

Section: Introductionmentioning

confidence: 99%

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

Liu

Yang³

2020

IEEE Access

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In this paper, a parametric approach to design a Luenberger functional observer for linear time-varying (LTV) systems with time-delay is investigated. Based on the solution to generalized Sylvester equation (GSE), the complete general parametric expressions for the functional observer gain matrices are established with the time-varying coefficient matrices, the time-varying closed-loop system and a group of arbitrary parameters. With the parametric method, the observation error system can be transformed into a linear system with the expected eigenstructure. Finally, a numerical simulation is provided to illustrate the effectiveness of the parametric approach. INDEX TERMS Functional observers, LTV systems with time-delay, parametric method, Sylvester equation.

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LP-based observer design for switched positive linear time-delay systems

Cited by 18 publications

References 40 publications

A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

A New Iterative Learning Control With Time Delays for LTI Systems in Frequency Domain

Stabilization of a class of switched systems with state constraints via time-varying Lyapunov functions

Linear Function Observers for Linear Time-Varying Systems With Time-Delay: A Parametric Approach

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