Finite frequency fault estimation observer design for T-S Fuzzy discrete-time descriptor systems

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.

ABSTRACTThis paper presents a robust observer‐based control design for one‐sided Lipschitz non‐linear systems with finite frequency specifications. The objective is to co‐design the observer and controller matrices to achieve asymptotic stability and disturbance attenuation within a specified finite frequency domain, encompassing low, middle, or high frequencies. The proposed approach leverages Finsler's lemma and Parseval's theorem to develop novel sufficient conditions expressed as Linear Matrix Inequalities (LMIs). These conditions ensure effective disturbance rejection in the specified frequency ranges. Notably, the computational approach employs a decoupling technique to linearize the bilinear terms, avoiding the need for additional assumptions on system matrices, and making the bilinear matrix inequalities (BMIs) conditions solvable with standard LMI tools. Two examples illustrate the effectiveness of the suggested control scheme.

formula omitted] state feedback controller design for continuous-time T–S fuzzy systems in finite frequency domain

The problem of finite frequency (FF) H∞ full-order filtering design for discrete-time linear systems, with polytopic uncertainties, is investigated in this paper. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma and a parameter dependent Lyapunov function, a set of sufficient conditions for the existence of the H∞ filter are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level from disturbance to the estimation error is minimized in the FF domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we apply Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance, and we show how we can calculate the filter gain matrices by using these conditions. Numerical example is given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.

This study is concerned with the fault detection problem for fractional‐order linear systems with disturbances. The and performance indices of fractional‐order systems in finite frequency domains are applied to measure the fault sensitivity and the disturbance robustness. A fractional‐order fault detection observer is designed to satisfy the two finite frequency performance indices simultaneously. Based on the generalised Kalman–Yakubovich–Popov lemma and the projection lemma, the design conditions are obtained in terms of linear matrix inequalities. Compared with the existing full frequency approaches, the proposed finite frequency one can get better results when the frequency ranges of faults and disturbances are known. The effectiveness of the proposed method is validated by numerical examples.

This brief addresses the problem of control for active vehicle suspension systems in finite frequency domain. The performance is used to measure ride comfort so that more general road disturbances can be considered. By using the generalized Kalman-Yakubovich-Popov (KYP) lemma, the norm from the disturbance to the controlled output is decreased in specific frequency band to improve the ride comfort. Compared with the entire frequency approach, the finite frequency approach suppresses the vibration more effectively for the concerned frequency range. In addition, the time-domain constraints, which represent performance requirements for vehicle suspensions, are guaranteed in the controller design. A state feedback controller is designed in the framework of linear matrix inequality (LMI) optimization. A quarter-car model with active suspension system is considered in this brief and a numerical example is employed to illustrate the effectiveness of the proposed approach.

This paper deal with the problem of the fault detection (FD) filter design for continuous-time switched systems with actuator faults. The actuator faults and the unknown disturbances of the system are set in finite frequency domain. By using the switched Lyapunov function and the average dwell-time (ADT) techniques, efficient conditions are obtained, which can realize the residual signal sensitive to the fault and robust to the unknown disturbances. In the design of fault detection filter, we use Linear matrix inequalities (LMIs) conditions to guarantee the finite frequency H∞ and H - performance index. Finally, a practical example is provided and simulation results are conducted to demonstrate the effectiveness of the proposed approach.

formula omitted] fault detection observer design for fractional-order singular systems in finite frequency domains

A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities

A finite element frequency domain method for 2D photonic crystals

Acoustic foam wedge panels provide good sound absorption qualities in the mid and high frequency ranges. In this study, a finite element frequency domain acoustical analysis is used for analysis. Such a numerical method is more efficient than the earlier studies by saving the calculation time on the elements of the incident acoustic field. During the design of a wedge panel, the cross-sectional width and the area of one section of the wedge panel are kept the same throughout the study. By varying the wedge angle, the maximum sound absorption capability of the wedge foam can be found. It is concluded that in the interested frequency regions, 100–4000 and 2000–4000 Hz, the wedge foam with wedge angle of 31° has the excellent sound absorption capability.

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

This paper investigates the dynamic output-feedback control problem for active suspension systems subject to actuator faults in finite frequency domain. Unmeasured states and uncertain parameters are considered in the controller design process. By using the generalized Kalman-Yakubovich-Popov (KYP) lemma, an H ∞ controller can be obtained in specific frequency band. The H ∞ controller is used to make passengers ride comfort under road disturbance. Moreover, the constraints of active suspension systems can be guaranteed depended on the designed controller. Finally, simulations are presented to illustrate the effectiveness of the proposed controller.

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

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.