Formula omitted] state feedback controller design for continuous-time T–S fuzzy 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.

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 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.

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.

This paper deals with the problem of fault estimation observer design for T-S fuzzy nonlinear discrete-time descriptor systems in the finite frequency domain. First, a novel fault estimation observer for the augmented descriptor system is given. Based on Parseval's theorem and Lyapunov theory, the performance in the finite frequency domain is derived via time-domain method. Then, new sufficient conditions of admissibility and robust performance index for the dynamic error system are obtained as bilinear matrix inequalities. Meanwhile, an iterative linear matrix inequality algorithm is given to obtain the optimal solution. Finally, an example is given to demonstrate the effectiveness of our method.

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

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.

In this paper, the stability of Markov jumping neural network (MJNN) with mixed delays under the control of finite frequency domain Parallel Distributed Compensation (PDC) controller is studied. By introducing the generalized-KYP lemma, the frequency domain analysis is combined with the neural network. The positive definite and negative definite conditions in Lyapunov stability theory are improved by using Bessel-Legendre inequality method. Sufficient conditions for the stability of the system are given and proved. Finally, numerical examples show that the system can maintain stability under the control of the PDC controller at low, medium and high frequencies.

This paper deals with the problem ofH∞model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FFH∞model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposedH∞model reduction design, a numerical example is given.

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 article generalises the Kalman--Yakubovi[cbreve]--Popov (KYP) lemma in delta domain to treat some conditions on different restricted frequency ranges. The frequency ranges are characterised by two quadratic forms. This characterisation encompasses low/middle/high frequency conditions for delta operator systems. By utilising the obtained delta domain generalised KYP lemma, a fault detection filter design problem is dealt with for delta operator systems in finite-frequency domain. The fault detection filter design problem is formulated as a two-objective optimisation algorithm with H − and H ∞ performance indexes. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

This paper introduces an $H_\infty$ fuzzy control synthesis method for a nonlinear large-scale system with a reduced number of linear matrix inequalities (LMIs). It is well known that a nonlinear large-scale system can be transformed to a Takagi–Sugeno (T–S) fuzzy system by using “sector nonlinearity” or “local approximation in fuzzy partition spaces” methods. Next, in order to achieve the fuzzy control design for this T–S fuzzy system, we solve the stabilization conditions that are represented by the LMIs. However, if the number of LMIs is large, the control design process may become very complicated. In this study, based on the Lyapunov method and S -procedure, several theorems are proposed for the synthesis of parallel distributed compensation (PDC)-type fuzzy control such that the nonlinear large-scale system achieves $H_\infty$ control performance, and the number of LMIs to be solved is reduced explicitly. As a result, the control design process will become much easier. Furthermore, if the modeling error between the nonlinear system and T–S fuzzy system exists, the robust $H_\infty$ control performance and the number reduction of LMIs are also achieved by the proposed theorem. Several examples are presented in this paper to show the number reduction effect of LMIs and the effectiveness of the proposed controller synthesis.

This paper studies model predictive control for a Takagi–Sugeno (T–S) fuzzy system with randomly occurring actuator saturation and packet losses. The nonlinearity of the actuator saturation is transformed into a set of convex hulls, while the packet losses are assumed to obey the rules of Bernoulli distribution. Both parallel-distributed-compensation (PDC) and non-parallel-distributed-compensation (non-PDC) strategies are adopted to design the controller for the system. In addition, sufficient conditions of the stability for the closed-loop system are given in terms of linear matrix inequalities. It is shown that the non-PDC strategy behaves less conservatively than the PDC strategy in controlling the considered T–S fuzzy system, when the input and output constraints are explicitly considered. Two simulation examples are provided to illustrate the effectiveness of the proposed design techniques.