Linear Matrices Inequalities Research Articles

Further results on stability analysis of delayed neural networks via a parameter-dependent quadratic function negative-definiteness lemma

This paper investigates the stability problem of delayed neural networks (DNNs) with time-varying delay. In the stability analysis of DNNs, the stability conditions are usually in form of second-order polynomial functions with respect to the time delay, which are nonlinear matrices inequalities and difficult to deal with. In order to obtain the stability criteria in terms of linear matrices inequalities (LMIs), some quadratic function negative-definiteness lemmas (QFNDLs) are proposed and widely employed. However, the research about QFNDL is still facing two challenges: large conservativeness and difficulty of optimisation. To overcome the challenges, this paper proposes a parameter-dependent quadratic function negative-definiteness lemma (PDQFNDL) to find the negative-definiteness condition. Compared with existing QFNDLs, the proposed lemma has two advantages: (i) Two moving points are introduced and the whole search interval is divided into two parts by an adjustable parameter, which contribute to the less conservativeness of stability criteria. (ii) The search interval of the adjustable parameter is smaller than the existing QFNDLs and the time of optimisation process is decreased. The proposed lemma is utilised to derive the less conservative stability criteria for DNNs based on a suitable Lyapunov–Krasovskii functional (LKF). Finally, the effectiveness and superiority of proposed stability criteria are demonstrated by several numerical examples.

Finite‐time exponentially extended dissipative filtering for singular time‐delay Markov jump systems with quantized outputs based on hidden Markov mode

AbstractThis article investigates finite‐time exponentially extended dissipative filtering for singular Markov jump systems with time‐varying delays and quantized outputs. The filter and quantizer are both mode‐dependent and their modes are asynchronous with the system modes, which are described by hidden Markov model. A more general performance index named as finite‐time exponentially extended dissipativity is employed to make the concept of extended dissipativity in infinite‐time domain suitable for the finite‐time case. With the aid of a series of novel and effective schemes, sufficient conditions are established to guarantee that the filtering error dynamics are finite‐time stochastically bounded with the exponentially extended dissipative performance. An asynchronous filter is successfully designed by solving a set of linear matrices inequalities. Finally, numerical examples are given to demonstrate the effectiveness of proposed methods.

Recoil suppression of deepwater drilling riser systems via static output feedback control with memory

In the dangerous ocean situations, the deepwater drilling riser needs evacuate emergently to guarantee the safety of the structures. The bottom equipment of the lower marine riser package should be disconnected from the blowout preventer timely. In this case, the recoil response of the riser occurs, which may lead to potential safety risks of the structure. This paper deals with the recoil suppression control problem of a deepwater drilling riser system via static output feedback recoil control scheme with memory. First, for the riser-tensioner system subject to the friction resistance of drilling discharge and the heave motion of platform, a static output feedback recoil controller with both current and delayed output signals of the system is proposed. Then, the existence conditions and design algorithm of the static output feedback recoil controller are derived. The gain matrices of the recoil controller can be obtained by solving linear matrices inequalities. It is found through simulation results that (i) the static output feedback recoil controllers with and without memory are effective to reduce the recoil responses of the riser; and (ii) to design the applicable output feedback recoil controllers, the displacement and velocity signals of the first mass block of the riser are required, and specifically, the velocity signal of the first mass block is indispensable; and (iii) the output feedback recoil controllers with memory provide more implementation options, and practically better than the ones without memory and some existing full state feedback recoil controllers.

Robust stabilization for an autonomous underwater vehicle motion based on descriptor time-delay model

This article introduces a new technique for stabilizing autonomous underwater vehicles in the descriptor model. Autonomous underwater vehicle stabilization is limited by several constraints, including time-variable uncertainty, time delay, and disturbances. The interaction of descriptor system requirements and the issues mentioned above adds complexities. This study outlines the delay-dependent [Formula: see text] robust stability achieved through memory-less and memory state feedback. Furthermore, a less conservative sufficient condition is obtained for admissibility using a new delay-dependent linear matrices inequality. Autonomous underwater vehicle is regular, impulse-free, and stable under all permissible conditions and satisfies prescribed [Formula: see text] performance conditions via a Lyapunov functional approach. The method applies to neutral and retarded dynamics with discrete and distributed time delays.

Robust Fault Estimation of Vehicular Yaw Rate Sensor Using a Type-2 Fuzzy Approach

In this article, a proportional integral (PI) fault observer is introduced due to its accuracy and expeditiousness. Considering the time-varying vehicle speed and other uncertain parameters in vehicle dynamics system, a type-2 fuzzy model is proposed to describe the system nonlinearity. Moreover, it could also address the problem of uncertainty in the membership function, which resulted from the parameter uncertainty. In addition, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> technique is studied to attenuate the effect of disturbance on the estimation performance and a set of linear matrices inequalities are obtained. The particle swarm optimization (PSO) approach is then adopted to find solutions to the PI fault observer. Finally, a simulation test is carried out based on the experimental data, which are collected from an electric vehicle. The simulation results demonstrate the effectiveness of the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }/PSO$</tex-math></inline-formula> method.

Adaptive controller design for uncertain singular systems with actuator failure

In this paper, the problem of model reference adaptive controller design with actuator failure is solved for a series of uncertain singular systems. The research on partial actuator failure is relatively mature and it is necessary to solve the problem of how to guarantee the system performance when the actuator fails completely. For this reason, we treat the system with actuator failure as a switching system with two subsystems and then solve the stability analysis problem of the error switching system. The emphasis is to design the adaptive controller by some sufficient linear matrices inequalities (LMIs) conditions and obtain the global stability criterion of the error switching system through the resident time method. Finally, the proposed method is applied to HiMAT aircraft to illustrate the feasibility and effectiveness of this kind of problem.

Model-based fault detection filter for Markovian jump linear systems applied to a control moment gyroscope

We study a fault detection problem in the context of Markovian Jump Linear Systems (MJLS). The major contribution of this paper is the design of a mode-dependent mixed H∞/H− Fault Detection Filter (FDF) under the MJLS formulation, which is obtained by solving a Linear and Bilinear Matrices Inequalities (LMI / BMI) optimization problem. As a secondary contribution, we present a simulation of the theoretical results using a Control Moment Gyroscope unit, which is extensively used as an actuator for attitude control of spacecraft and satellites. The attitude control of satellites is a class of problem that is within the framework of MJLS, since it allows us to model the loss of communication between the various components of the network system. Therefore, designing Fault Detection Filters under this framework provides reliable solutions. From the simulations results, it is possible to observe that the proposed mixed H∞/H− fault detection solution outperformed the approach using only the H∞ norm, showing that it could be a valuable alternative for the fault detection problem.

Asynchronous finite-time state estimation for semi-Markovian jump neural networks with randomly occurred sensor nonlinearities

This paper addresses the finite-time state estimation problem for semi-Markovian jump neural networks with sensor nonlinearities under the consideration of leakage delay and time-varying delay. The modes of original system and desired estimator are supposed to be asynchronous. Some sufficient conditions are proposed to guarantee the finite-time boundedness as well as mixed H∞ and passive performance of the error system in terms of constructing Lyapunov–Krasovskii functionals. By utilizing affine Bessel-Legendre inequalities, a less conservative result can be achieved. By virtue of linear matrices inequalities approach, the asynchronous state estimator gains are obtained. Two numerical examples are provided to demonstrate the less conservativeness and effectiveness of our method.

Robust feedback controller in finite frequency based on H∞ performance for a variable speed wind turbine

The modern wind turbine system is modelled as a flexible structure operating in the presence of wind speed turbulences. Furthermore, it's highly nonlinear and its dynamic changes rapidly with the change of wind speed. A sophisticated control system is needed to allow wind turbines to generate power in a wide variety of wind conditions. This paper investigates a system control in finite frequency based on H∞ performance in order to maximise the extracted energy from the wind while mitigating aerodynamic loads. The finite frequency approach is used to design a robust feedback control to stabilise the system when the disturbances occur in a finite frequency band due to the stochastic nature of the wind flow. The controller gains are given in terms of linear matrices inequality (LMIs) which can be solved easily using existing numerical tools. The performance of the proposed control strategy is investigated in terms of stability and robustness under variable wind speed, and illustrated by tests simulation using MATLAB® software.

Adaptive observer-based H∞ FTC for T-S fuzzy systems. Application to cart motion model

In this paper, an adaptive observer-based fault-tolerant control (FTC) strategy is proposed for a class of Takagi-Sugeno (T-S) fuzzy systems with both actuator and sensor faults under external disturbances. FTC approach is developed to compensate the actuator faults and to stabilize the faulty system. Furthermore, using H∞ optimization technique, an adaptive fuzzy observer is developed, not only to achieve a simultaneous estimation of system states, sensor and actuator faults, but also to attenuate the influence of disturbances. In terms of linear matrices inequalities (LMIs), sufficient conditions of the existence of observer and controller are derived. We overcome the drawback of two-step algorithm by proposing a single-step one which allows to solve only the strict LMIs. Therefore, the obtained results present an acceptable compromise between conservatism reduction and computational complexity. Finally, two numerical examples which one of them is an application to a cart motion model are presented to demonstrate the usefulness of the proposed method.

\mathcal{H}_{\infty} control for fuzzy markovian jump systems based on sampled-data control method

This paper investigates the problems of \begin{document}$ \mathcal{H}_{\infty} $\end{document} performance analysis and sampled-data control about fuzzy Markovian jump systems. Firstly, in order to make full use of the information of both intervals \begin{document}$ x(t_{k}) $\end{document} to \begin{document}$ x(t) $\end{document} and \begin{document}$ x(t) $\end{document} to \begin{document}$ x(t_{k+1}) $\end{document} , we construct the mode-dependent Lyapunov function, which consists of a two-sided closed-loop function. Built on the above Lyapunov function, the stochastically stable conditions with less conservative are given by using linear matrices inequalities (LMIs). Then, a state feedback controller is presented for the studied systems. At last, an example is offered to illustrate the efficiency of our main results.

On Interval Observer Design for Continuous-Time LPV Switched Systems

State estimation for switched systems with time-varying parameters has received a great attention during the past decades. In this paper, a new approach to design an interval observer for this class of systems is proposed. The scheduling vector is described by a convex combination so that the parametric uncertainties belong into polytopes. The considered system is also subject to measurement noise and state disturbances which are supposed to be unknown but bounded.The proposed method guarantees both cooperativity and Input to State Stability (ISS) of the upper and lower observation errors. Sufficient conditions are given in terms of Linear Matrices Inequalities (LMIs) using a common quadratic Lyapunov function. Finally, a numerical example is provided to show the effectiveness of the designed observer.

Fault Compensation Controller for Markovian Jump Linear Systems

Abstract In this paper, we tackle the fault-compensation controller in the context of Marko-vian Jump Linear Systems (MJLS). More specifically, we propose the design of H∞ Fault-Compensation Controllers under the MJLS formulation, which is provided in terms of linear matrices inequalities optimization problems. These particular controllers have as the main motivation the network communication loss which is inherent to any automation process. We present a numerical example of a coupled tank system, where a Monte Carlo simulation illustrates the feasibility of the proposed solution. The results show that the proposed approach is indeed a valuable alternative to compensate for the fault occurrence.

Finite-time Fault Detection Filtering for Switched Singular Systems with All Modes Unstable: an ADT Approach

This paper finishes the fault detection (FD) problem for switched singular systems with all subsystems unstable. Considering the particularity of singular systems, the regularity and impulse-free property analysis on it are carried out. Utilizing a time-driven switching strategy, a switching signal is proposed and the finite-time stability is guaranteed firstly. Then, with the help of discretized Lyapunov function, a piecewise Lyapunov function is employed to accomplish the finite-time boundedness with L2-gain analysis. Through transferring the fault detection filters design into the L2-gain analysis, we can obtain the existence conditions of the FD detector via linear matrices inequalities (LMIs). Finally, the effectiveness and validity are illustrated by two examples.

Formula omitted] performance for delayed singular nonlinear Markovian jump systems with unknown transition rates via adaptive control method

We work on the investigation of the H∞ performance for uncertain stochastic singular Markovian jump systems with both nonlinear external disturbance and general unknown transition rates (TRs) in this paper. There exist uncertainties in both parameters and TRs. Every transition rate could be totally unavailable or only its estimated value is available. With a generalized H∞ disturbance attenuation level γ, some robust controllers are designed such that the delayed singular Markovian jump system is stochastically admissible. The novel controllers designed in this paper consist of an adaptive controller and a linear controller. Moreover, some sufficient linear matrices inequalities (LMIs) conditions are provided according to Lyapunov stability theory and Itoˆ’s differential formula. Finally, an example is presented to demonstrate our main results.

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.

Mixed H2/H∞ Fault Detection Filter for Markovian Jump Linear Systems

We tackle the mixed H2/H∞ fault detection filter problem for a Markov jump linear system (MJLS) in the discrete-time domain. We present three distinct formulations: the first one is to minimize an upper bound on the H2 subject to a given upper value on the H∞ norm; the second one is the opposite situation; that is, we minimize an upper bound on H∞, subject to a given restriction on the H2 norm; and the third one is the minimization of a weighted combination of the upper bound of both the H2 and H∞ norms. We present new conditions in the form of linear matrices inequalities (LMI) that provide the design of the fault detection filter. We also present results for the so-called mode-independent case and the design of robust H∞ filters in the sense that the system matrices are uncertain. In order to illustrate the feasibility of the proposed approaches, a numerical example is presented.

Adaptive Observer and Fault Tolerant Control for Takagi-Sugeno Descriptor Nonlinear Systems with Sensor and Actuator Faults

This paper concerns the problem of state, fault estimation (FE) and Fault Tolerant Control (FTC) of Takagi-Sugeno (T-S) descriptor systems affected by sensor, actuator and external disturbances simultaneously. An Adaptive Fuzzy Observer is firstly proposed to achieve a simultaneous estimation of descriptor system states, actuator and sensor faults by using the H∞ optimization technique. A FTC is secondly proposed to stabilize the faulty descriptor system. Based on Lyapunov method, stability analysis and design conditions of the resulting closed-loop system are formulated in a set of Linear Matrices Inequalities (LMIs). The adaptive fuzzy observer and the FTC are independently designed, in order to avoid the coupling problem. Accordingly, the observer and controller gains are computed separately by solving a set of LMIs and then used to estimate the unmeasured states, sensor and actuator faults at the same time. Finally, a truck-trailer system application is given to illustrate the validity of the proposed approach.

A model reference tracking based on an active fault tolerant control for LPV systems

SummaryThis work deals with the problem of a model reference tracking based on the design of an active fault tolerant control for linear parameter‐varying systems affected by actuator faults and unknown inputs. Linear parameter‐varying systems are described by a polytopic representation with measurable gain scheduling functions. The main contribution is to design an active fault tolerant controller whose control law is described by an adaptive proportional integral structure. This one requires 3 types of online information, which are reference outputs, measured real outputs, and the fault estimation provided by a model reference, sensors, and an adaptive polytopic observer, respectively. These types of information are used to reconfigure the designed controller, which is able to compensate the fault effects and to make the closed‐loop system able to track reference outputs in spite of the presence of actuator faults and disturbances. The controller and the observer gains are obtained by solving a set of linear matrices inequalities. Performances of the proposed method are compared to another previous method to underline the relevant results.

Adaptive Fuzzy Observer-Based Fault-Tolerant Control for Takagi–Sugeno Descriptor Nonlinear Systems with Time Delay

This paper investigates the problems of state/fault estimation and active fault-tolerant control (AFTC) design for time-delay descriptor fuzzy systems subject to external disturbances and actuator faults. Using Takagi–Sugeno fuzzy models, an adaptive fuzzy observer is proposed to achieve system state and actuator fault estimation simultaneously. According to Lyapunov functional method, design and analysis conditions of the resulting closed-loop delayed descriptor system are formulated in terms of linear matrices inequalities (LMIs). Observer and controller gains are computed by solving a set of LMIs in only one step and then used to both estimate the unmeasured states and actuator faults in AFTC context. Numerical examples are provided to show the merit and the conservativeness of the proposed approach in comparison with the existing methods by considering various types of actuator faults.