시변 지연시간을 갖는 이산 구간 시변 시스템의 시변 불확실성의 안정범위

한형석 ( Hyung-seok Han ) 한국항행학회 2017 韓國航行學會論文誌 Vol.21 No.6

본 논문에서는 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 지연 상태변수에 존재하는 불확실성 안정범위에 관한 것을 다룬다. 고려된 시스템은 지연 없는 상태변수에 대한 시스템 행렬이 구간범위에서 시변으로 변동하고, 지연 시간이 구간범위 내에서 시변인 지연 상태변수에 대하여 비구조화된 불확실성이 시변으로 존재하는 시스템이다. 기존의 많은 연구들이 시변에 대한 부분을 고려하지 못하고 시불변 경우에 대하여 얻어진 것에 반하여, 본 논문에서는 모든 요소를 시변으로 고려하여 새로운 안정범위를 도출하였다. 새로운 안정범위는 적용 가능한 시스템에 대한 제한이 없는 것으로 그 효용성이 기존의 결과 보다 우수하다. 제안된 범위는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 이용하는 복잡한 과정이 필요하지 않다. 수치예제를 통하여 제안된 결과가 기존의 결과들을 포함할 수 있음을 보이고, 이들 보다 확장성과 효용성이 우수함을 확인한다. In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

시변 지연시간을 갖는 이산 구간 시변 시스템의 안정조건

한형석 ( Hyung-seok Han ) 한국항행학회 2016 韓國航行學會論文誌 Vol.20 No.5

본 논문에서는 상태변수에 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 안정조건을 새롭게 제안한다. 고려한 시스템은 지연 없는 상태변수에 대한 시스템 행렬과 지연 상태변수에 대한 시스템 행렬이 시변 구간 행렬로 표현되며, 지연시간도 구간에 대하여 시변인 특성을 갖는다. 제안된 안정조건은 리아프노프 안정 이론을 이용하여 유도되며, 매우 간단한 부등식의 형태로 표현된다. 본 논문에서는 기존의 시불변 구간 행렬의 안정성 문제를 시변 구간 행렬의 안정성 문제로 확장하고, 기존에 발표된 결과를 포함하는 강력한 안정조건이 유도된다. 이 안정조건의 유도과정에서는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 구하지 않아도 된다. 또한, 기존의 결과들과의 비교를 통하여 제안된 안정조건이 많은 기존 안정 조건들을 포함할 수 있음을 보인다. 기존 수치예제를 일반적인 형태로 확장하였고 이에 대하여 새로운 안정조건의 확장성과 효용성을 확인한다. In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

시변 시간지연 함수를 위한 시뮬레이션 객체의 구성

최순만 한국마린엔지니어링학회 2004 한국마린엔지니어링학회지 Vol.28 No.4

Time delays are included in most of actual systems, and some of which are shown as time varying. To analyze the time varying time delay system in the time domain, a useful delay module to express the function as a tool is much helpful to get corresponding outputs under given conditions. A method is proposed here to design the algorithm of time delay module for simulation or control purposes, including the problems of initializing and reallocating data in buffer. After classifying the time varying time delay into the distributed mode and lumped mode, an object to describe delay module is configured and tested under the defined input signal and given time delay variation. The simulation results show that the output of module matches reasonably with the case of real system.

Finite-time Consensus of Leader-following Multi-agent Systems with Multiple Time Delays over Time-varying Topology

Fenglan Sun,Mingyan Tuo,Jürgen Kurths,Wei Zhu 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.8

This paper studies the finite-time consensus of leader-following multi-agent systems with multiple time delays over time-varying topology. The finite-time consensus protocol based on the agents’ states and the communication topology is designed. By adopting the algebraic graph theory, Lyapunov stability theory and pinning control method, some sufficient conditions for the finite-time consensus are given. It is proved that the system can reach consensus in a finite time both over the connected and disconnected topology. Moreover, the upper bound of the convergence time is given. Several simulations are presented to verify the effectiveness of the adopted method.

Stochastic Stability for a Class of Discrete-time Switched Neural Networks with Stochastic Noise and Time-varying Mixed Delays

Ying Cui,Yurong Liu,Wenbing Zhang,Fuad E. Alsaadi 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.1

In this paper, stochastic stability is analyzed for a class of discrete-time switched neural networks, in which time-varying mixed delays and stochastic noise are considered. Specifically, benefitting from the triple summation term included in a new Lyapunov functional, time-varying distributed delays are tackled and a criterion of decay estimation for a non-switched neural network is firstly obtained. Subsequently, in view of average dwell time methodology and stochastic analysis, several sufficient conditions are obtained to ensure that the stochastic stability problem is solvable. Furthermore, the derived sufficient conditions reflect that the decay rate of the considered neural networks has a close relationship with average dwell time, upper and lower bounds of delays and intensity of stochastic noise. Finally, validity of the inferred conclusions is given by a simulated example.

H∞ Filtering for Discrete-Time Systems with Time-Varying Delay

Huanshui Zhang,Wei Wang,Chunyan Han 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.6

The problem of H∞ filtering for discrete-time systems with time-varying delay in measurement is investigated in this paper. First, under the assumption that the time-varying delay is of a known upper bound, the delayed measurement is re-described as the one with multiple state delays. Then the proposed H∞ filtering problem is transformed into one for systems with multiple measurement chan-nels that contain the same state information as the original measurement and each channel has a single constant delay. Finally, based on the reorganized innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of an H∞ filter which guarantees a prescribed attenuation level is derived. The solution to the H∞ filtering is given in terms of the solutions to Riccati and matrix difference equations.

기반 기술 : 시변 지연시간을 갖는 이산 구간 시스템의 안정조건

한형석 ( Hyung-seok Han ) 한국항행학회 2015 韓國航行學會論文誌 Vol.19 No.6

본 논문에서는 상태변수에 시변 지연시간이 있는 선형 이산 구간 시스템의 안정조건을 고려한다. 고려한 시스템은 시스템 행렬과 지연 상태변수에 대한 시스템 행렬이 구간 행렬로 표현되며, 지연시간도 구간에 대하여 시변인 특성을 갖는다. 제안된 안정조건은 리아프노프 안정 이론에 의하여 유도되며 매우 간단한 부등식의 형태로 표현된다. 기존의 시불변 구간행렬의 안정성 문제를 시변 지연 시간을 갖는 시스템으로 확장한 것이다. 더불어, 새로운 안정조건은 시불변 경우에 대하여 연구된 기존 결과를 포함할수 있으며, 구간 시변 지연 시간과 시스템의 안정성과의 연관관계를 나타내는 것이다. 제안된 조건은 구간시스템에 대한 교란 변수의 크기를 구하는 문제에도 응용될 수 있다. 수치예제를 통하여 새로운 안정조건의 효용성을 확인할 수 있으며, 기존에 발표된결과들과의 비교도 이루어진다. The stability condition of linear discrete interval systems with a time-varying delay time is considered. The considered system has interval system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. Compared to previous results, the stability issue on the interval systems is expanded to time-varying delay. Furthermore, the new condition can imply the existing results on the time-invariant case and show the relation between interval time-varying delay time and stability of the system. The proposed condition can be applied to find the stability bound of the discrete interval system. Some numerical examples are given to show the effectiveness of the new condition and comparisons with the previously reported results are also presented.

Robust IMC-PID and Parameter-varying Control Strategies for Automated Blood Pressure Regulation

Shahin Tasoujian,Saeed Salavati,Matthew Franchek,Karolos Grigoriadis 제어·로봇·시스템학회 2019 International Journal of Control, Automation, and Vol.17 No.7

The present work focuses on comparing a robust and a parameter-varying control design approach forautomatically regulating blood pressure in critical hypotensive patients using vasopressor drug infusion. Meanarterial pressure (MAP) response of a patient subject to vasoactive drugs is modeled by a first-order dynamicalsystem with time-varying parameters and a time-varying delay in the control input which limits the implementationof conventional control techniques. Two methods are examined to address the variability and the time-varying delayof the physiological response to the drug. First, a Padé approximation is used to transform the infinite-dimensionaldelay problem into a finite-dimensional model represented in the form of a non-minimum phase (NMP) system. Asystematic parameter-varying loop-shaping control is proposed to provide the closed-loop system with stability andtracking performance in the presence of measurement noise and disturbances. Second, an internal model control(IMC) strategy is examined to design a fixed proportional-integral-derivative (PID) controller cascaded with a lagcompensator by considering the time-varying model to be a perturbed uncertain system. To account for systemuncertainty, the small-gain theorem is employed by which robust stability conditions are investigated. The proposedcontrol methods are applied to critical hypotensive patient resuscitation to regulate MAP while considering thelimitations posed by the time-varying parameters of the physiological response model and the large time-varyingdelay. Simulation results are provided and compared to evaluate the performance of the proposed control actionsunder various hypotensive scenarios.

Finite-time Control for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

Yanli Ruan,Tianmin Huang,Kun Zhou 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.5

This paper focuses on the problem of finite-time control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and norm-bounded disturbance. By constructing a new augmented Lyapunov-Krasovskii functional, a delay-dependent finite-time boundedness criterion is derived for the T-S fuzzy time-delay system by aid of the auxiliary function-based integral inequalities and the reciprocally convex combination technique. Then, based on the parallel distributed compensation scheme, a state feedback controller is designed to ensure finite-time boundness of the closed-loop T-S fuzzy system, which can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Delay-Range-Dependent and Delay-Distribution-Independent Stability Criteria for Discrete-Time Singular Markovian Jump Systems

Falu Weng,Wei-Jie Mao 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.2

The problem of delay-range-dependent stability for discrete-time singular Markovian jump systems with time-varying delay is discussed in this paper. Based on time-delay partitioning technique, a new delay-range-dependent Lyapunov functional is established firstly. Then, based on the probability idea, LMIs-based delay-range-dependent and delay-distribution-independent conditions are proposed for the system to be regular, causal, and stochastically stable. Furthermore, in terms of solving a set of coupled LMIs, the stabilizing controller is obtained such that the closed-loop system is regular, causal, and stochastically stable. Finally, numerical examples are given to show the results derived from the proposed methods are less conservative than the existing ones.