Systems In Finite-frequency Domain Research Articles

Asynchronous fault detection filtering design for continuous-time T-S fuzzy affine dynamic systems in finite-frequency domain

This paper investigates the problem of asynchronous fault detection filtering design for continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems in finite-frequency domain. The objective is to design an admissible piecewise affine filter such that the asymptotic stability of the filtering error system with the prescribed finite-frequency H−/H∞ performance can be guaranteed. It is assumed that the premise variables of the plant are unmeasurable so that the filter state transition and the plant state transition may be asynchronous. By applying the celebrated S-procedure, the generalized Kalman-Yakubovič-Popov lemma is extended such that the finite-frequency H−/H∞ performance of the fuzzy affine filtering error system is ensured. Furthermore, by utilizing piecewise quadratic Lyapunov functions, Projection lemma, and some matrix inequality linearization techniques, the finite-frequency fault detection filtering design approach is developed for the concerned T-S fuzzy affine dynamic system. It is shown that sufficient conditions for the existence of the fault detection filter are formulated as feasibility of a set of linear matrix inequalities. Finally, the effectiveness and advantages of the proposed design approach are illustrated by simulation studies.

Distributed fault detection for uncertain Lipschitz nonlinear multi‐agent systems in finite frequency domain

AbstractThis article focuses on distributed fault detection for uncertain Lipschitz nonlinear multi‐agent systems (MASs). To handle parameter uncertainties, a finite‐frequency unknown input observer (UIO) is designed to formulate the reference residual system and based on it, a robust UIO corresponding to the fault detection system is designed using an model matching approach. In the UIO constructed for one agent, the unknown input composed of faults in the other agents and disturbances in the whole system is partitioned to decouple part of them, which avoids the constraint of the rank condition of UIO and allows for fault detection for more than one faulty agent. The generated residual is sensitive to the corresponding fault while robust against the nondecoupled unknown input and parameter uncertainties, of which the design conditions are transformed into a set of linear matrix inequalities (LMIs). A numerical simulation is conducted to illustrate the effectiveness of the proposed method.

Robust DOF control for uncertain polynomial fuzzy systems in finite frequency domain

This study addresses the issue of robust dynamic output feedback control (DOF) for polynomial Takagi–Sugeno (T–S) fuzzy systems in the Finite Frequency (FF) domain. Sufficient conditions for designing the robust DOF control are derived in terms of the sum of squares (SOS). The proposed strategy is built in the FF domain to reduce conservation-generated by the techniques established in the whole frequency domain. In addition, there are no transformation matrices or equality constraints under these conditions, which simplifies the numerical solution. To show the validity of the suggested technique, several numerical examples are presented.

Event‐triggered fault detection for discrete‐time Markovian jump systems in finite frequency domain

AbstractThis paper is concerned with the design of the finite frequency fault detection (FD) filter based on the event‐triggered scheme (ETS) for discrete‐time Markovian jump (DMJ) systems with Lipschitz functions, time‐varying delays, and packet dropouts. A novel FD filter subject to ETS and data missing is developed, and the augmented filter system is rewritten as a DMJ‐linear parameter varying (DMJ‐LPV) system through a reformulated Lipschitz property. Then, two novel lemmas are proposed to guarantee the DMJ‐LPV system robust to unknown disturbances and sensitive to finite frequency faults. Next, the proposed lemmas are deduced into linear matrix inequalities by using Finsler's lemma and S‐procedure. Finally, the application of Chua's circuit system is employed to illustrate the validity and superiority of the proposed theory.

Event-triggered H–/L∞ fault detection observer design for discrete-time Lipschitz nonlinear networked control systems in finite-frequency domain

This paper proposes an event-triggered fault detection observer (FDO) design method for discrete-time Lipschitz nonlinear networked control systems (NCSs) in finite-frequency domain. First, a discrete event-triggered transmission scheme is proposed to mitigate the utility of limited network bandwidth. Second, with the aid of a reformulated Lipschitz property, the nonlinear error dynamics are converted into a linear parameter varying (LPV) networked system model. Third, based on this model, the finite-frequency index is used to measure the worst-case fault sensitivity performance and the norm from unknown disturbance to residual is used to measure disturbance robustness performance. Next, a residual evaluation and a dynamic threshold are synthesised based on the norm. Furthermore, sufficient conditions of the FDO design are derived and transformed by a set of linear matrix inequalities (LMIs). The proposed FDO design method can significantly reduce the data transmission to relieve the communication pressure, and can also achieve better FD performance than the full frequency domain. Finally, A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

H∞ control for uncertain one‐sided Lipschitz nonlinear systems in finite frequency domain

SummaryThe current article discusses the H∞ disturbance attenuation control design problem for one‐sided Lipschitz systems in finite frequency domain. Models containing norm‐bounded parameter uncertainties, disturbances, and input nonlinearities are considered. By contrast to existing full frequency methods, the H∞ controller is computed depending on the frequency ranges of disturbances. The finite frequency disturbance attenuation index is initially defined. Thanks to Finsler's lemma, sufficient and less conservative analysis conditions are also derived for the closed‐loop system. Then, synthesis conditions in the low, middle, and high frequency ranges as well as the whole frequency range, are formulated in terms of linear matrix inequalities. At last, to prove the effectiveness and the superiority of the proposed approach, a physical example is used and a comparative study is done.

Fault Detection Filtering Design for Discrete-Time Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain

This article focuses on the problem of fault detection filtering design for discrete-time interval type-2 Takagi-Sugeno (T-S) fuzzy systems in finite frequency domain. Considering the fact that external disturbances and faults are usually reside in finite frequency ranges, the finite frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> performances are introduced to reflect the disturbance robustness and fault sensitiveness in finite frequency domain, respectively. Based on discrete-time Fourier transform and its properties, finite frequency performance analysis results are first obtained. Then, by exploiting the information on upper and lower membership functions, the membership-function-dependent filtering design conditions in the form of linear matrix inequalities are established for discrete-time interval type-2 T-S fuzzy systems in finite frequency domain. With the obtained filter, a fault detection scheme is then proposed and it is shown that the resulting fault detection system is asymptotically stable with prescribed finite frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> performances. Finally, the effectiveness of the proposed method is validated by simulation studies.

Quantized $H_\infty$ Output Control of Linear Markov Jump Systems in Finite Frequency Domain

Incorporating the disturbance frequency into system analysis and synthesis, this paper is dedicated to the quantized ${H_\infty }$ static output control of linear Markov jump systems. The output quantization is transformed into a sector bound form, and the finite frequency performance is handled by Parseval’s theorem. With the aid of Finsler’s lemma, sufficient conditions for the resulting closed-loop system are first established to satisfy the required finite frequency performance. To treat the static output feedback control problem in the framework of linear matrix inequalities, a new strategy is developed to decompose the coupling among Lyapunov variables, controller gain, and system matrices. In contrast to the existing results in the literature, no additional assumptions are imposed on the system matrices. Numerical examples are presented to demonstrate the validity of the established results.

Fault estimation and active fault-tolerant control for discrete-time systems in finite-frequency domain

The active fault-tolerant control (FTC) problem for discrete-time systems in finite-frequency domain is addressed based on faults’ estimation. By the descriptor system approach, the observers are designed such that the stability and H∞ performance index of dynamic error systems are analyzed in finite frequency domain. The estimation of faults is obtained by the designed observers. By using the estimation of faults, a H∞ FTC method is presented to show the stability analyses of closed-loop systems in term of GYP lemma. Numerical simulations are given to demonstrate proposed FTC methods’ effectiveness.

Fault detection for vehicle active suspension systems in finite‐frequency domain

This study solves a new fault detection strategy for vehicle active suspension systems in finite-frequency domain. Three fault detection filters are constructed in different finite frequency domains, which ensure that the error between residuals and faults is minimum. The H ∞ filter problem is used to figure out the design problem of fault detection. The conditions of residual systems meeting H ∞ performance are obtained by considering generalised Kalman-Yakubovich-Popov lemma and stability theory. The problem of filter design is solved by an optimisation algorithm. Illustrative examples are given to show the proposed design method's effectiveness and potential.

Actuator and sensor faults estimation for discrete-time descriptor linear parameter-varying systems in finite frequency domain

ABSTRACTThis paper investigates the problem of fault estimation for discrete-time descriptor linear parameter-varying systems with actuator faults, sensor faults and external disturbances. First, in order to estimate the actuator and sensor faults simultaneously, an augmented system is constructed, where the auxiliary state vector consists of the original state vector and the sensor fault vector. Then, considering the fact that many faults usually occur in finite frequency ranges, a novel fault estimation observer with finite frequency specifications is designed, where the conservatism can be reduced compared with the traditional fault estimation design methods in full frequency domain. By employing the generalised Kalman–Yakubovich–Popov lemma and two finite frequency H∞ performance indices, the sufficient conditions of the proposed observer are given in terms of linear matrix inequalities. Furthermore, by using slack variables, improved results on the fault estimation observer design are obtained, which are convenient to calculate fault estimation observer parameters for different frequency ranges. An example is presented to illustrate the effectiveness of the proposed method.

L2-gain filter design for continuous-time LPV systems in finite frequency domain

Abstract This paper provides an approach for synthesizing gain-scheduled and robust filters for linear parameter-varying continuous-time systems in finite frequency ranges with guaranteed L2-gain performance. The technique is based on the well-known generalized KYP lemma, which relates frequency-domain inequalities to semi-definite constraints. The time-varying parameters are assumed to be measurable online and, furthermore, to have known bounds of variation. Filtering design conditions with guaranteed L2-gain performance are proposed in the form of parameter-dependent linear matrix inequalities (LMIs), which can be solved in terms of LMI relaxations. Numerical examples borrowed from the literature illustrate the advantages (improved performance) of the proposed approach when compared to other available methods.

Sensor fault estimation for Lipschitz nonlinear systems in finite-frequency domain

ABSTRACTIn this study, the problem of sensor fault estimation observer design for Lipschitz nonlinear systems with finite-frequency specifications is investigated. First, the sensor fault is considered as an auxiliary state vector and an augmented system is established. Then, by transforming the nonlinear error dynamics into a linear parameter varying system, a sufficient condition for the observer-error system with a finite-frequency H∞ performance is derived in terms of linear matrix inequalities (LMIs). Based on the obtained condition, novel nonlinear observers are designed to simultaneously estimate the system states and the fault signals and attenuate the disturbances in the finite-frequency domain. The proposed design method can provide less restrictive LMI conditions and get a better disturbance-attenuation performance when the frequency ranges of disturbances are known beforehand. A numerical example is given to show the effectiveness and superiority of the new results.

Event-triggered fault detection for discrete-time Lipschitz nonlinear networked systems in finite-frequency domain

The problem of event-triggered fault detection (FD) filter design for discrete-time Lipschitz nonlinear networked systems with finite-frequency specifications is investigated. The event-triggered transmission scheme is introduced to mitigate the utility of limited network bandwidth. The developed filter combines the H∞ and H− indices. For this class of systems, the generalized Kalman–Yakubovic–Popov lemma-based finite-frequency FD filter design methods are invalid. To solve this problem, the nonlinear error dynamics are transformed into a linear parameter varying (LPV) system based on the use of a reformulated Lipschitz property and a new lemma is developed to capture the system performances in finite-frequency domain. By introducing slack variable techniques, sufficient conditions for the design of FD filter are derived in terms of linear matrix inequalities (LMIs). The proposed design method can significantly reduce the data transmission and achieve a better FD performance than that in full frequency domain. Finally, two examples are presented to validate the effectiveness and superiority of the new results.

Fault detection for switched T-S fuzzy systems in finite frequency domain

This paper is concerned with the problem of the fault detection for switched T-S fuzzy systems with actuator faults. The system faults and unknown disturbances are considered to be in a finite frequency domain. An effective fault detection filter is designed to measure the fault sensitivity and disturbance robustness. By using Parseval’s theorem and S-procedure, a new finite frequency method of fault detection for switched T-S fuzzy systems is formulated. Sufficient linear matrix inequalities (LMIs) conditions are proposed to design the fault detection filter, which can guarantee the finite frequency $H_{-}$ and $H_{\infty}$ performance. The effectiveness of the given finite frequency method for switched T-S fuzzy systems is illustrated through two numerical simulation examples.

A fault detection observer design for LPV systems in finite frequency domain

This paper addresses the fault detection observer design problem for linear parameter-varying systems. Two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness. First, the H− index fault sensitivity condition in finite frequency domain is obtained by generalised Kalman–Yakubovich–Popov lemma and new linearisation techniques. Then, with the aid of Kalman–Yakubovich–Popov lemma and projection lemma, the stability and robustness conditions are derived. It turns out that the non-convexity problem which is caused by dealing with the above three conditions can be translated into a bilinear matrix inequality optimisation problem by increasing the dimensions of slack variable matrix. An iterative linear matrix inequality algorithm is proposed to get the solution. The effectiveness of the filter is shown via three numerical examples.

Fault Detection for Discrete-Time Switched Systems in Finite-Frequency Domain

This paper is concerned with the fault detection (FD) problem for a class of linear discrete-time switched systems in finite-frequency domain. The fault detection filters (FDFs) with switching mech...

H ∞ switching filter design for LPV systems in finite frequency domain

This article studies the problem of finite frequency H ∞ filter design for switching linear parameter varying (LPV) systems with disturbance frequency affected by system parameters. A set of switching filters are designed, each suitable for a specific parameter subregion and a specific finite frequency performance index. A hysteresis switching logic is adopted, and the design problem is finally formulated into linear matrix inequality (LMI) which can be solved efficiently with LMI Control Toolbox. A numerical example is given to illustrate the effectiveness of the proposed method.

Nonfragile filtering for discrete-time linear systems in finite-frequency domain

This article investigates the problem of nonfragile filter design for discrete-time linear systems subject to noises with known frequency ranges. Additive interval uncertainty reflecting imprecision in filter implementation is considered. By the aid of generalised KYP lemma, both deterministic and randomised filtering algorithms are proposed to deal with noises in low-, middle- and high-frequency domain, respectively. The proposed nonfragile finite-frequency filters can get a better noise attenuation performance when frequency ranges of noises are known beforehand. An example about F-18 aircraft model is given to illustrate the effectiveness of the proposed algorithms.

A stable fault detection observer design in finite frequency domain

This article addresses the stable fault detection observer design problem for linear time-invariant continuous-time systems in finite-frequency domain. The fault detection filter design is a synthesised optimal Luenberger observer that guarantees two requested performance indexes of fault sensitivity and stability. With the aid of generalised Kalman–Yakubovich–Popov lemma and increasing dimensions of slack variable matrix, the stability and H − performance analysis of the closed-loop system with a fault detection observer has been translated into a convex linear matrix inequality (LMI) optimisation problem to avoid the complexity of system associated with weight functions. An iterative LMI algorithm has been presented for the fault detection observer design. The effectiveness of proposed approaches is demonstrated by two numerical examples.