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In this paper, the problem of multi-objective control for active suspension systems with polytopic uncertainty is addressed via $H_{\infty }/GH_{2}$ static output feedback with a limited-frequency characteristic. For the overall analysis of the performance demanding both the vehicle-ride comfort related to vertical- and transversal-directional dynamics and the time-domain constraints related to the driving maneuverability, a seven-degree-of-freedom full-vehicle model with an active suspension system is investigated. The robust static output-feedback control strategy is adopted because some state variables may not be directly measured in a realistic implementation. In designing this control, the finite-frequency $H_{\infty }$ performance using the generalized Kalman-Yakubovich–Popov lemma is optimized to improve the passenger’s ride comfort, while the $GH_{2}$ performance is optimized to guarantee the constraints concerning the suspension deflection limitation, road-holding ability, and actuator saturation problem. This control synthesis problem is formulated as non-convex bilinear matrix inequalities and requires simultaneous consideration of different finite-frequency domain ranges for vertical and transversal motions for evaluating the $H_{\infty }$ performance. These design difficulties are overcome by the proposed multi-objective quantum-behaved particle swarm optimizer, which efficiently explores the relevant trade-offs between the considered multiple performance objectives and eventually provides the desired set of Pareto-optimal solutions. Further, the numerical simulation cases of a full-vehicle active suspension system are presented to illustrate the effectiveness of the proposed control synthesis methodology in both frequency and time domain.

Drag-free control technology plays a key role in space science tasks such as microgravity science, space basic physics verification, Earth observation, and spacecraft high-precision navigation. At present, a drag-free controller is designed in the time domain aimed at the full frequency band by many scholars, which cannot meet some of the high-precision task requirements under specific frequency constraints. Therefore, some scholars use robust control and quantitative feedback control to design a controller in the frequency domain indirectly, but the design process is complicated. Moreover, the satellite tracking test mass strategy is generally used, and it limits the control capability of a drag-free satellite with double test masses. For these problems, a design method of a finite frequency domain controller based on Generalized Kalman-Yakubovich-Popov (GKYP) lemma combined with frequency separation control strategy is presented in this paper, which covers the dynamic model, design of the finite frequency H∞ controller, proof of stability, and performance analysis. Finally, the numerical simulation analysis is carried out. The simulation results show that the controllers are effective. [ABSTRACT FROM AUTHOR]

In this paper, novel fault estimation and fault-tolerant control methods are proposed for dynamics of high-speed train based on descriptor systems with uncertainties in finite frequency domain. Dynamics of high-speed train is established based on multi-particle model considering that basic resistance is seen as the coefficient of state variables, and additive resistance and the operating noise are seen as multi-source disturbance. Concurrent actuator, sensor faults, and wind gust are considered simultaneously; wind gust is modeled as a disturbance generated by the exogenous system, and an uncertain descriptor system with actuator fault and the exogenous disturbance is established by seeing the sensor fault of high-speed train as the state variables. A robust disturbance-observer-based fault estimation method is proposed to decouple the non-linearity of the descriptor system, so that the combining estimation of the fault and wind gust is implemented. This observer has an unknown input structure, and its gain matrices are formulated as linear matrix inequalities. The observer not only guarantees the augmented state estimation error is asymptotic stable but also the actuator fault estimation and wind gust estimation errors are robust to the multi-source disturbance and the uncertainties. Based on the estimation results, the fault-tolerant controller associated with the state estimation, faults estimation, and wind gust estimation results is proposed to implement a stable close-loop fault-tolerant control for dynamics of high-speed train. Simulation examples are given to illustrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

This article investigates the problem of fault detection filtering for two dimensional (2-D) continuous-discrete systems with multi state delay in finite frequency domain. Firstly, by the Lyapunov-Krasovskii functional (LKF) method, a finite frequency bounded real lemma (BRL) is presented. Secondly, based on the obtained finite frequency BRL, an observer-based finite frequency fault detection filter is provided as a residual generator, which is used to simultaneously minimize the disturbance effect and maximize the fault effect in finite frequency ranges. Finally, simulations confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in an unbounded medium R d ( d ⩾ 1), we first use the (Floquet-)Bloch transform to formulate an equivalent variational problem in a bounded domain. By investigating the source term's projection onto certain periodic functions, the second-order model can then be derived via asymptotic expansion of the Bloch eigenfunction and the germane dispersion relationship. We establish the convergence of the second-order homogenized solution, and we include numerical examples to illustrate the convergence result. [ABSTRACT FROM AUTHOR]

In this paper, the control problem is concerned for a class of continuous-discrete T-S fuzzy systems (TSFSs) described by the Roesser model with a finite frequency (FF) specification. Assume that the frequencies of the disturbance input are known in advance and dominated within a FF range. An performance is established within a FF range for continuous-discrete TSFSs, which is an extension of the standard performance. This paper aims to construct a state feedback controller which guarantees the closed-loop system to be stable and to have a prescribed FF performance. A numerical tractable method for designing a controller is obtained through matrixing, thus giving conveniently the expression of controller with linear matrix inequality as tool kit. [ABSTRACT FROM AUTHOR]

In this paper, a self-triggered saturated model predictive control (SMPC) for Markov jump system (MJS) is studied in finite-frequency domain. First, the MJS with multi-modes is transformed into a single mode system with embedded transition probability to prepare for the use of generalized Kalman–Yakubovich–Popov (GKYP) lemma. Second, a dynamic self-triggered mechanism with time-varying threshold is developed to predict the next triggering time according to the current time, states, and jumping mode. Third, for disturbances that only possess finite-frequency band, a co-design of triggering condition and SMPC is realized by properly employing GKYP lemma. Compared with existing works, the main motivation of this paper is to improve the anti-interference ability within a specified frequency range. Moreover, we also aim to shorten the gap between the finite band control theory and its applications to practical engineering problems. Finally, the effectiveness of the proposed approach is demonstrated by both the numerical and practical simulations. [ABSTRACT FROM AUTHOR]

The paper focusses on the model reduction of discrete-time switched linear systems with finite-frequency specifications. First, we propose a performance index that can estimate systematic performance over finite frequency. And then, we use GKYP (generalized Kalman–Yakubovich–Popov lemma) and introduce some relaxation matrices with variable parameters to analyse the problem in different situations. Based on the above conditions, sufficient conditions can be obtained for meeting the index of finite frequency. Finally, we illustrate two numerical examples. The results show that the proposed method can improve approximation performance. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of fault estimation for two-dimensional (2-D) Fornasini-Marchesini (FM) dynamical systems. The objective of this paper is to design a fault estimation filter to reconstruct the characteristics of faults in low-frequency domain and satisfy different performance levels. Utilizing the generalized Kalman-Yakubovich-Popov (GKYP) lemma, this problem is transformed into a multi-objective optimization problem, which is non-convex in essence. On this basis, an optimization algorithm is proposed to solve the non-convex optimization problem. Sufficient conditions are derived for the proposed fault estimation filter. Finally, simulation results show the effectiveness of the theoretical results.

This research investigates the synthesis of a new Finite Frequency Observer (FFO) to detect faults affecting wind turbines. First, the wind turbine nonlinear behaviour is approximated using Takagi-Sugeno (T-S) fuzzy modelling technique for observer design purposes. Then, through the H-/H∞ optimisation technique with Finite Frequency (FF) specification, the FFO design conditions are formulated using the Lyapunov method as a set of LMIs. Finally, to assess the efficiency of the FFO-based detection approach, simulations results are applied to a dynamic 4.8 MW WT model, where an Unknown Input Observer method is used for comparison. [ABSTRACT FROM AUTHOR]

This paper proposes an event-triggered H − / L ∞ 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 H _ / L ∞ index is used to measure the worst-case fault sensitivity performance and the H _ 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 L ∞ 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. [ABSTRACT FROM AUTHOR]

This paper studies the problem of path tracking of Autonomous Ground Vehicles (AGVs) in the presence of sideslip angles. An observer is designed to estimate both the sideslip angle and the vehicle yaw rate, based on which an observer-based controller is established such that the closed-loop system is stable and the vehicle follows a desired path accurately. In particular, the nonlinear vehicle dynamics model is reformulated as a Linear Parameter Varying (LPV) system, and a finite frequency H ∞ criteria is satisfied such that the disturbances are attenuated effectively, the parameter-dependent gain matrices are calculated simultaneously by solving a convex optimization problem. Simulation results show the effectiveness of the method proposed. • The measurement of vehicle states including positions and headings is apt to be affected by external disturbances. • An observer-based path tracking controller is designed for autonomous vehicles. • The vehicle model is reformulated as an LPV system. • Both the observer and controller gains are parameter-dependent and are obtained simultaneously. [ABSTRACT FROM AUTHOR]

This 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. [ABSTRACT FROM AUTHOR]

This paper addresses the robust finite frequency (FF) H∞ distributed filtering problem for uncertain networked control system (NCS) that consists of heterogeneous subsystems. By using past output measurements and considering the frequency information of disturbance signals, the designed distributed memory filter is able to guarantee that the filtering error system is well‐posed, stable and has the FF H∞ performance. Based on the extended finite frequency bounded realness lemma for uncertain NCSs, the existence condition of robust FF H∞ distributed memory filter is derived. Moreover, it is shown that by taking advantage of more past output measurements of NCS, the proposed design procedure can derive a distributed filter that achieves a lower H∞ performance bound. Finally, a practical example is given to show the effectiveness of the proposed filter design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H1 gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H1 gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite frequency fault detection (FD) for a class of T-S fuzzy systems with partly unmeasurable premise variables. To fully use the available information of the considered T-S fuzzy system, an FD observer whose premise variables consist of the measurable premise variables and the estimations of unmeasurable ones of the fuzzy model is designed. However, the membership functions of the fuzzy model and the observer to be designed are unsynchronized, such that the existing FD methods based on parallel distribute compensation (PDC) strategy may be infeasible. To overcome this difficulty, a novel non-PDC H ∞ / H − unknown input observer is designed to achieve the purpose of fault detection and provide less conservative results. Finally, two simulation examples are given to illustrate the validity and merits of the presented FD scheme. [ABSTRACT FROM AUTHOR]

Generally, distributed H ∞ filtering approach achieves a certain disturbance attenuation level in the full frequency range. However, the energy of system noise or reference input usually limits in a specified frequency range. To reduce such a design conservatism, this article develops a distributed filtering approach based on dual scale, that is, filtering over a finite-time interval from time scale and also on a specified finite-frequency region from the frequency scale. Our target is to make the filtering error under sensor networks monitoring be relaxed into an ellipsoid bound rather than asymptotically converging to zero for exogenous noise in a specified frequency range. Finally, two illustrative examples demonstrate the strength of the developed filtering approach. [ABSTRACT FROM AUTHOR]

This paper investigates the fault detection problem for two dimensional (2-D) continuous discrete state-delay Roesser systems in finite frequency domains. Two performance indexes H∞ and H- are used to measure the fault sensitivity and the disturbance robustness in finite frequency. Based on this, the fault detection problem is converted into a filtering problem by designing a filter to generate a residual signal. By the generalized KYP lemma, convex design conditions are obtained, which are expressed in terms of linear matrix inequalities (LMIs). An example is provided to demonstrate the feasibility and effectiveness of the proposed method.

This paper is concerned with the asynchronous fault detection and isolation (FDI) strategy in finite frequency domain for Markov jump systems (MJSs) with actuator failures under networked environment. A set of binary-valued Bernoulli distributed sequences is introduced to describe the transmission and the scheduling of the sensor nodes. Then, an MJS directing by two Markov process and with multiple stochastic parameters is derived to characterize the whole system dynamics. Subsequently, by means of the stochastic $\mathcal {H}_{-}$ index in finite frequency domain and the geometric mapping approach, an asynchronous FDI scheme is investigated, in which the filters complete the FDI mission with only partial information of the measurements. Meanwhile, each FDI filter is only sensitive to one possible actuator fault and decoupled from others. Then the existence of the desired filters is ensured by some novel sufficient conditions. Finally, an application example is presented to show the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the fault detection of two-dimensional Fornasini Marchesini (FM) system. It is assumed that the FM system has a sensor fault, and the fault is modeled as multi-mode: no fault mode and fault mode. The generalized Kalman-Yakubovich-Popov(KYP) Lemma is used and the tangent plane method is used to deal with the coupling term. The results of research show that the FM system meets certain performance indexes. The research conclusion shows the effectiveness of the proposed fault detection method by numerical simulation. [ABSTRACT FROM AUTHOR]

To address the advanced driver assistant system (ADAS) in practical application with some disturbances, we propose a novel finite frequency $H_\infty $ observer-based method in this study, which enables effectively object tracking to restrain the disturbance during middle and low frequency ranges. We first analyze the Radar tracking characteristics. Then, an $H_\infty $ observer is established. Based on the $H_\infty $ theory and Kalman-Yakubovič-Popov (KYP) lemma, the design criterion of the finite frequency $H_{\infty }$ observer is established by a linear matrix inequality (LMI). Lastly, two real world experiments are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the generalised Kalman-Yakubovich-Popov (GKYP) lemma and its application in finite frequency (FF) H ∞ distributed filter design for networked control systems (NCSs). The network communication channels between subsystems are considered to be affected by uncertainties. Firstly, based on the proposed linear matrix inequality characterisation for an FF region and S-procedure, a GKYP lemma is presented for NCSs. After that, the FF bounded realness and FF positive realness in terms of individual subsystems are studied as special cases of the proposed GKYP lemma. Moreover, as an application of the developed GKYP lemma, the FF H ∞ distributed filtering problem for nonideally interconnected NCS is studied. Finally, illustrative examples are given to show that the developed EF methods have less conservation than the common method over the entire frequency region. [ABSTRACT FROM AUTHOR]

In this paper, a neural network-based event-triggered fault detection scheme is addressed within the finite-frequency domain for a class of nonlinear Markov jump system. Initially, an approximation model based on multilayer neural network to alternate the nonlinear Markov jump system is constructed. For the purpose of saving the communication network bandwidth, a transmission mechanism based on the event-triggered strategy is subsequently applied in which each signal is transmitted depending on the designed condition rather than the sampling period. Further, two theorems with considering the signal frequency and the applied event-triggered mechanism are derived which guarantee the fault sensitivity as well as disturbance attenuation for the augment systems in certain frequency ranges. Then, the desired filters can be synthesized by the linear solvable conditions that are derived with the aid of the previous theorems and some novel decoupling techniques. Eventually, the proposed algorithm's efficiency is shown by a presented computational example. [ABSTRACT FROM AUTHOR]

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.

Summary: This article aims at solving the problem of robust H−/H∞ fault detection (FD) over finite frequency domain for spatially interconnected systems (SISs) with polytopic uncertainties. A fault detection observer is designed to generate the residual signal, and in order for the observer to work, the well‐posedness, robust stability, and finite frequency H−/H∞ indexes are properly defined for the error systems. A sufficient condition for the well‐posedness and robust stability of error systems is given based on the theory of continuous semigroup. Then, to obtain the H−/H∞ performance indexes conditions, a reformed generalized Kalman‐Yakubovich‐Popov (GKYP) lemma for polytopic SISs is derived, which takes the noncasual structure of SISs into account. It turns out that the reformed GKYP lemma is an extension of some existing results in traditional multidimensional casual systems. By resorting to Finsler's lemma and a linearization technique, the existence conditions of finite frequency H−/H∞ FD observer for polytopic SISs are given in terms of linear matrix inequalities. An illustrative example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this research, a multi-objective frequency domain-constrained static output feedback control is developed for the delayed active suspension system with wheelbase preview information. Firstly, the model of the half-vehicle active suspension system with wheelbase preview information and time delay is constructed by employing the augmented method. Secondly, in vertical vibration, the human body senses are more intense when the frequency of the external disturbance is in the range of 4–8 Hz. Therefore, a finite frequency control method is proposed for the controller design with robust H ∞ and generalized H 2 performance. Thirdly, considering that a full online knowledge of states is not available in practical suspension systems, a static output feedback strategy is proposed to guarantee the feasibility of the controller by using a two-stage method. Finally, simulation study is given to explain the effectiveness and superiority of the presented controller. [ABSTRACT FROM AUTHOR]

This paper proposes an H - / H ∞ fault detection observer method for a class of spatially interconnected time-delay systems (SITSs) with interconnected chains in finite frequency domain. As one of the main contribution, a delay-dependent generalized Kalman–Yakubivich–Popov (GKYP) lemma for SITSs with interconnected chains is proposed. Based on the giving GKYP lemma, sufficient conditions for the existence of the observers to guarantee the fault sensitivity and disturbance robustness in finite frequency domain are presented. Finally, an example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: The 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 ℒ2 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. [ABSTRACT FROM AUTHOR]

This paper deals with the design problem of a robust fault estimation (FE)/ faulttolerant control (FTC) scheme for wind turbines (WT) in the finite frequency domain (FF). First, an adaptive fuzzy H8 observer is constructed to simultaneously reconstruct the WT states and faults within the FF range. Throughout the observer analysis, it is only assumed that faults, uncertainties, and disturbances are bounded, which coincide with the practical requirements. In the second stage, based on the observer information, an active FTC method is proposed to stabilize the faulty WT. The controller and observer gain matrices are extracted employing the Lyapunov theory, where constraints are expressed as a set of linear matrix inequalities (LMIs). The Simulation results illustrate the best performances of the suggested strategy. [ABSTRACT FROM AUTHOR]

This brief addresses a controller/fault detector and scheduling protocol codesign scheme in the finite frequency domain for a class of constrained networked systems. By considering the data transmission in both sensor-control center and control center-actuator channels, a switched stochastic system is first modeled. With the aid of the mode-dependent average dwell time, sufficient conditions are subsequently investigated to capture the desired performances including the finite frequency one, in which the relationship between the node accessing rate and the performances is developed. Then, node-dependent controller/fault detectors and the scheduling protocol are codesigned by the derived conditions. Finally, an application to the High Alpha Research Vehicle (HASV) is given to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In order to alleviate the deterioration on control effect caused by the inertia mass and the time-delay of a rack and pinion electromagnetic actuator, a finite frequency dynamic output feedback H∞ time-delay control strategy is proposed in this article. Currently, a H∞ controller is generally designed with the objective to minimize the infinite norm of the transfer function from the external disturbance to the control output, and the values of the slack coefficients are obtained according to the experience. But when used in practical, problems are found that only small external disturbance energy and narrow scope of driving conditions are allowed and it is difficult to find the optimal solution just according to the experience. In allusion to these problems, a H∞ controller design method with the objective to maximize the allowable external disturbance energy is proposed, and genetic algorithm is used to optimize the values of the slack coefficients. Finally, bench tests are carried forward to verify the control effects of the two controllers. The tests results show that, the controller designed with the objective to maximize the allowable external disturbance energy can adapt to more severe driving conditions, and it is more significant in actual application on vehicles. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the frequency‐dependent fault detection scheme for networked systems under uniform quantization and try‐once‐discard protocol scheduling. By considering the communication constraint and the data node scheduling, a switched system is firstly modeled to characterize the dynamic features of the whole system. The switching function of the derived system is determined by the try‐once‐discard protocol. For this class of system, a sufficient condition to ensure the exponentially ultimately boundedness is established. With the aid of some novel analysis processes, sufficient conditions to characterize the desired finite frequency performances, which transform the frequency‐domain restrictions into time‐domain conditions, are subsequently developed. Then, the fault detection filters corresponding to the transmission nodes are synthesized by solving an optimization problem. Finally, an application to VTOL aircraft is presented to illustrate the effectiveness of the proposed fault detection strategy. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of delay‐dependent H∞ filtering for spatially interconnected time‐delay systems (SITSs) with interconnected chains in finite frequency domains. First, a multidimensional (N‐D) hybrid time‐delay Roesser model and a delay‐dependent finite frequency bounded ream lemma (BRL) for SITSs with interconnected chains are proposed. Then, using the obtained delay‐dependent finite frequency BRL, a finite frequency H∞ filter design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, a practical example is provided to clearly demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• The T-S fuzzy method is used to approximate the nonlinear uncertain dynamics. • A finite frequency control criterion is formulated based on the Lyapunov theory. • A parallel-distributed compensation strategy is used in the fuzzy SOF controller. This paper investigates the problem of fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Firstly, as the physical suspension systems always exist the phenomenon of sprung and un-sprung mass variation and time delay, the Takagi-Sugeno (T-S) fuzzy model is adopted to represent the nonlinear uncertain active suspension system with uncertainties and time delay. Secondly, since the human body is much more sensitive to vertical vibrations between 4 and 8 Hz, a finite-frequency control criterion is formulated for the controller deign with consideration of time delay and output constraints. Other mechanical constraints such as suspension travel, tire dynamic deflection and actuator saturation are also considered. Thirdly, on a practical point of view, not all the states are online measurable. Hence, a novel fuzzy static output feedback (SOF) controller is proposed by applying the parallel-distributed compensation (PDC) scheme. The sufficient conditions for deriving the fuzzy SOF controller are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical simulations on a quarter-car suspension model are conducted to validate the effectiveness and applicability of the proposed fuzzy SOF controller. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A hybrid finite frequency controller is proposed for the vibration suppression of a large flexible structure mounted with collocated sensors and actuators. The controller has passive characteristics at low frequencies and small gain characteristics at high frequencies. Compared with a strictly positive real controller based on the standard Kalman–Yakubovich–Popov lemma, the hybrid finite frequency controller has less energy consumption but can obtain approximately identical performance. Furthermore, when the plant passivity is violated at high frequencies by noncollocation of sensors and actuators, the strictly positive real controller based on the Kalman–Yakubovich–Popov lemma is no longer able to attenuate the vibration of the large flexible structures, while the hybrid finite frequency controller is effective in suppressing the vibration and avoiding spillover instability. Simulation results are presented to validate the effectiveness of the hybrid finite frequency controller. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault detection observer design for discrete spatially interconnected time-delay systems (SITSs) in finite frequency range. Firstly, a delay-dependent generalised Kalman–Yakubivich–Popov (GKYP) lemma for SITSs is proposed. Then, by the giving GKYP lemma, a distributed fault detection observer design method can be derived by solving a set of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the finite frequency fault detection (FD) problem is addressed for a class of nonhomogeneous Markov jump systems with nonlinearities and sensor failures. Compared with the existing sensor fault models that contain many known faulty modes, the fault model in this paper is more general since it not only covers more types of sensor failures but also does not need to know the fault information in advance. Then, by means of finite frequency stochastic performance indices, a novel FD scheme is proposed. Some new lemmas, in which the nonlinear item and nonhomogeneous Markov switching are dealt appropriately, are developed to capture the stability of the system and desired finite frequency performances. Then, by the derived lemmas, sufficient conditions with potentially less conservativeness are investigated to guarantee the existence of the FD filters. Finally, an application to HiMAT vehicle is given to illustrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the finite-frequency bounded realness analysis and finite-frequency H ∞ distributed filter design problem for the discrete-time networked system which consists of heterogeneous subsystems interconnected over an arbitrary network. The H ∞ performance analysis of networked systems is generalized from the entire-frequency region to some finite-frequency regions. A necessary and sufficient condition in the centralized manner is established to check the finite-frequency bounded realness property of networked systems. Moreover, in order to design a distributed filter and reduce the computational effort, a sufficient condition in terms of individual subsystems is developed. Based on the new condition derived, a sufficient condition is given for the existence of the distributed filter and an LMI method is then presented for designing the distributed filter. A practical example is included to illustrate the proposed approach in this paper and it is shown that the developed finite-frequency bounded realness condition is less conservative than the existing entire-frequency one. [ABSTRACT FROM AUTHOR]

In this study, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media (including the source term) at finite frequencies and wavenumbers spanning the first Brillouin zone. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider the projection of germane Bloch wave function onto a suitable eigenfunction as descriptor of effective wave motion. For generality the finite wavenumber, finite frequency homogenization is pursued in Rd via second-order asymptotic expansion about the apexes of 'wavenumber quadrants' comprising the first Brillouin zone, at frequencies near given (acoustic or optical) dispersion branch. We also consider the junctures of dispersion branches and 'dense' clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the germane eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points that are relevant to the phenomenon of topological insulation. On the other hand, the effective model for nearby solution branches is found to invariably entail a Dirac-like system of equations that describes the interacting dispersion surfaces as 'blunted cones'. For all cases considered, the effective description turns out to admit the same general framework, with differences largely being limited to (i) the eigenfunction basis, (ii) the reference cell of medium periodicity, and (iii) the wavenumber- frequency scaling law underpinning the asymptotic expansion. We illustrate the analytical developments by several examples, including Green's function near the edge of a band gap and clusters of nearby dispersion surfaces. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the finite-frequency H ∞ control problem of active suspensions is investigated. In view of the human body is much sensitive to the vertical vibrations between 4 and 8 Hz, a robust finite-frequency state-feedback H ∞ controller is introduced to suppress the sprung vibration in the concerned frequency range. In order to simultaneously control the vehicle heave, roll, and pitch motions, a full-car suspension model is adopted. Suspension parameter uncertainties, actuator saturation, and suspension deflection constraints are all considered in the model, and a robust controller is designed to handle the parameter uncertainties and achieve the prescribed H ∞ performance. Simulation with different road conditions and parameter uncertainties are performed and the results illustrate the effectiveness of the proposed controller. Highlights • A full-car model is adopted to control the heave, pitch and roll motions. • The 4–8 Hz range disturbance is attenuated by a finite-frequency controller. • The parameter variations are considered to guarantee the system robustness. [ABSTRACT FROM AUTHOR]

This paper deals with the filter design problem of two-dimensional (2-D) discrete-time nonlinear systems described by Fornasini-Marchesini local state-space (FM LSS) model under Takagi-Sugeno (T-S) fuzzy rules. The frequency of disturbance input is assumed to be known and to reside in a finite frequency (FF) range. A novel so-called FF gain is defined for 2-D discrete-time systems, which extends the standard gain. The aim of this paper is to design filters such that the filtering error system is asymptotically stable and has the disturbance attenuation performance in sense of FF gain. Sufficient conditions for the existence of a desired fuzzy filter are established in terms of linear matrix inequalities (LMIs). Simulation examples demonstrate the technique and its advantage. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the problem of finite frequency (FF) H ∞ filter for nonlinear discrete-time systems in the Takagi-Sugeno (T-S) fuzzy models. The objective is to propose a new design sufficient condition via linear matrix Inequality (LMIs) formulations, ensuring that the filtering error system is stable and has a minimized H ∞ , performance when frequency ranges of noises are known beforehand. Less conservative results are obtained by using the generalized Kalman-Yakubovich-Popov (gKYP) lemma, Finsler's lemma and some independent matrices. An example about a tunnel diode circuit is given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. [ABSTRACT FROM AUTHOR]