Set Of LMIs Research Articles

State Estimation of Positive Switched Interval Systems with Metzler–Takagi–Sugeno Fuzzy Models

This paper addresses the problem of estimating the state of a class of interval and positive nonlinear switched systems. The considered system class is represented by Metzler–Takagi–Sugeno fuzzy switched models with positive Lipschitz nonlinear functions and bounded disturbance. The fuzzy switching interval observers need real-time measurable values of premise variables. The introduced design method in this paper allows us to compute the lower and upper bounds of the system state under assumption that unknown disturbances are norm-bounded, computing the observer gain to achieve such robustness. Formulations and proofs of the design condition for switching fuzzy positive interval observers document that the diagonal stabilisation principle is implementable by a common set of LMIs in the construction of strictly positive interval observer gains, guaranteeing Metzler and Hurwitz observer system matrices and positiveness of the lower and upper bounds of the estimated system states. Design conditions for the interval-switching observer structures are formulated via linear matrix inequalities to also ensure H∞-norm disturbance attenuation and corresponding Lipschitz parameter upper bounds. The proposed algorithm structures are informal and easily creatable as is illustrated by a numerical example.

Sliding mode control with integral sliding surface for linear uncertain impulsive systems with time delays

This paper devotes to the problem of sliding mode control (SMC) for linear uncertain impulsive systems with time delays and matched disturbances. An SMC scheme based on a novel integral-type sliding function with an impulse regulation term is proposed. The sliding function is designed so that the finite-time reachability of the sliding surface can be guaranteed for any given impulses. A linear delayed state feedback control law with switching gains is introduced to stabilize the resulting sliding mode dynamics, which is able to improve robust performance against parameter uncertainty. The existence conditions of the delayed state feedback control laws are derived by employing a piecewise discontinuous Lyapunov functional. It is shown that the desired switching gains can be obtained by solving a set of LMIs through a convex optimization procedure. Finally, the correctness and validity of the theoretical results are fully verified in a practical application with several different types of impulse inputs.

Exponential stabilisation of delayed Lur'e systems with multi-rate sampled-data control

In this paper, we focus on the multi-rate sampled-data based exponential stabilisation problem of delayed Lur'e systems. First, a merging time sequence is constructed from the sampling instants of multiple sensors to form the so-called analysis interval and the closed-loop system is represented by a system with multiple time-varying delays over the constructed analysis interval. Then, a useful estimation about the norm of the system state is established. On this basis, a stabilisation criterion is proposed by constructing a two-sided looped-functional. The proposed functional drops positive definite restrictions over the whole analysis interval . Therefore, it can reduce the conservatism of the derived criterion. And, the feasible solution of the multi-rate sampled-data controller gain can be provided by solving a set of LMIs. Finally, the given example shows the advantage of the main results.

Strong stabilization of high order plants

Designing stable feedback controllers that stabilize a given plant, known as strong stabilization, has been explored in the literature by using several algorithmic construction procedures. Many of these methods rely on step-by-step interpolation or solving an auxiliary H∞ control problem, or a set of LMIs. This paper gives an explicit construction of simple strongly stabilizing controllers for plants that have restrictive number of zeros in the extended right half plane, without any restrictions on the number or location of poles. A similar construction is also developed for the case of plants with restrictions on the poles. The order of the proposed stable controllers is at most one less than that of the plant, and they are computed by selecting just a few positive parameters determined from the H∞ norms of certain transfer functions.

On designing Lyapunov-Krasovskii functional for time-varying delay T–S fuzzy systems

In this work, we have investigated the problem of assessing stability and designing an appropriate feedback control law for T-S fuzzy systems with time-varying delay. By way of designing a new Lyapunov-Krasovskii functional based on Legendre polynomials and membership functions, we have developed conditions for stability assessment and feedback gain synthesis. The resulting algebraic conditions form a set of hierarchical LMIs which, by increasing the order of the Bessel-Legendre polynomial, compete with the sum of squares in both conservatism and complexity. Finally, two examples are provided to demonstrate the effectiveness of the findings.

Fuzzy observer-based fault detection for wind turbines using the finite-frequency approach

ABSTRACT 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.

Robust H∞ Network Observer-Based Attack-Tolerant Path Tracking Control of Autonomous Ground Vehicle

In this study, a robust H∞ network observer-based attack-tolerant path tracking control design is proposed for the autonomous ground vehicle (AGV) under the effect of external disturbance, measurement noise and actuator/sensor attack signals. At first, a more practical AGV system is applied to describe the interaction among the longitudinal speed, lateral speed and yaw rate. Based on Controller Area Network (CAN), the information of local AGV is transmitted to remote control center through wireless channel and then the control command can be calculated from remote control center. To avoid the corruption of actuator/sensor attack signal from insecure CAN, two novel smoothed signal models are introduced to describe these attack signals and are embedded with the AGV dynamics system as an augmented system. Subsequently these attack signals can be simultaneously estimated with the AGV system state by the conventional Luenberger-type observer of the augmented system. By using the estimated state and attack signals, a robust H∞ network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the energy of path tracking error and eliminate the influence of attacks signals. With the help of convex Lyapunov function, the design conditions of robust H∞ network observer-based attack-tolerant path tracking control design for AGV are derived in terms of a set of nonlinear difference inequalities. To reduce the difficulties in solving these nonlinear difference inequalities, Takagi-Sugeno fuzzy interpolation method is applied to approximate the nonlinear AGV system and the design can be simplified to a set of LMIs, which can be easily solved via LMI TOOLBOX in MATLAB. A double lance change task of AGV in CAN is provided as a simulation example to illustrate the design procedure and validate the effectiveness of proposed design method in comparison with the conventional steering control method.

Fault detection observer design in finite-frequency domain for networked interconnected systems

With the development of network technology, information can flow flexibly, and the research of interconnected systems are booming. The article proposes an H ∞ / H - fault detection observer design means for a networked interconnected system. First, convert a linear networked interconnection systems to linear network systems. Next, the H − index is accustomed to measuring the worst-case sensitivity to failure and H ∞ norm from ungiven inputs to residuals is accustomed to measure disturbance robustness performance, so that the residuals generated by the designed fault detection observer are sensitive to failures and robust to disturbance in finite-frequency domain. Besides, sufficient conditions of the observer design are derived and transformed by a set of LMIs. Lastly, numerical simulations are provided to demonstrate the correctness and effectiveness of the designed means.

Nonquadratic stabilization conditions for nonhomogeneous Markovian jump fuzzy systems with higher-level operation modes

This paper is concerned with the problem of designing a dissipative control for generalized nonhomogeneous Markovian jump fuzzy systems (MJFSs) that can cover both piecewise-homogeneous MJFSs and nonhomogeneous MJFSs through the use of dual modes, i.e., plant and higher-level modes. Based on a dual-mode-dependent fuzzy control law within a nonparallel distributed compensation (non-PDC) scheme, the nonquadratic stabilization conditions are first formulated in terms of multi-parameterized linear matrix inequalities (M-PLMIs), and then be transformed into a finite set of solvable LMIs without reducing M-PLMIs to PLMIs. Further, since the proposed relaxation technique can address the transition probabilities of plant and higher-level modes at once, the characteristics on mutual dependence between dual modes are fully incorporated into the nonquadratic stabilization conditions. Two illustrative examples are given to show the validity of the proposed approach.

Observer‐based preview repetitive control for uncertain discrete‐time systems

AbstractIn this paper, the preview repetitive control (PRC) problem is considered for uncertain discrete‐time systems subject to a previewable periodic reference signal. First, an augmented system including future information on the previewable reference signal is constructed. Second, considering the state unmeasured and periodic tracking reference signal, state observer and preview repetitive controller (PRCr) are designed in both state feedback and output feedback settings. To achieve signal tracking performance, a two‐dimensional (2D) model approach and some LMI technique are presented to describe the control and learning actions of the PRC system by using the lifting technique. Then, by Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of LMIs, and meanwhile, the design of a repetitive controller with preview actions is proposed through the LMI approach. Finally, two examples illustrate the effectiveness of the results.

Design of H∞ state estimator for delayed static neural networks under hybrid-triggered control and imperfect measurement strategy

This paper address the problem of designing H∞ state estimator for a class of delayed static neural networks (DSNNs) under the hybrid-triggered scheme (HTS) and imperfect measurement strategy. Firstly, for reducing the redundancy of signal transmission together with saving the network resource, a HTS is introduced in DSNNs, where the HTS characterized by Bernoulli distribution and takes into account the inevitable network-induced delay and packet dropout phenomenon simultaneously. Then, without loss of generality, we extend the results to a more general dissipative property, which is proposed for the first time, and which contains strict passivity except for the traditional four cases. Further, by considering the HTS, a modified delay-product-type Lyapunov functional is proposed. Accordingly, sufficient conditions for global asymptotically stable with a prescribed level γ of augmented system are obtained in the light of a set of LMIs, and the explicit expression of expected estimator is given. Finally, the feasibility and availability of the results of development are verified by three cases as example.

Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.

Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.

Detection‐based weighted LFC for multi‐area power systems under DoS attacks

This study is concerned with resilient load frequency control (LFC) scheme design of multi-area power systems with communication delay and aperiodic denial-of-service (DoS) attacks. First, to identify DoS attacks, a detection mechanism in the actuator side is proposed which is a time counter measuring the input delay. The identified DoS attacks are constrained by its upper bound of frequency and duration. When DoS attacks are identified, actuator switches to zero-input strategy from hold-input strategy. According to the switching control inputs, switched time delay system model is established to describe the attack influence on LFC system. Further, a criterion of preserving weighted performance is derived by combining piecewise Lyapunov–Krasovskii functional method with switched system method. Based on the criterion, the resilient control gain is designed by solving a set of LMIs. Finally, numerical simulations are given to verify the validness of the attack detection based resilient LFC scheme.

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

ABSTRACTThis paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.

Finite‐Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

The finite‐time synchronization control is studied in this paper for a class of nonlinear uncertain complex dynamic networks. The uncertainties in the network are unknown but bounded and satisfy some matching conditions. The coupling relationship between network nodes is described by a nonlinear function satisfying the Lipchitz condition. By introducing a simple Lyapunov function, two main results regarding finite‐time synchronization of a class of complex dynamic networks with parameter uncertainties are derived. By employing some analysis techniques like matrix inequalities, suitable controllers can be designed based on the obtained synchronization criteria. Moreover, with the obtained control input, the time instant required for the system to achieve finite‐time synchronization can be estimated if a set of LMIs are feasible or an assumption on the eigenvalues of some matrices can be satisfied. Finally, the effectiveness of the proposed results is verified by numerical simulation.

Dynamic reset output feedback with guaranteed convergence rate

We propose a new output feedback reset control architecture for linear continuous-time plants, where the dwell-time parameter corresponds to a quantified interval of time where the controller state and the plant input are freezed, thus providing a constant plant input. For this new architecture we first prove a stability and performance analysis test, based on certain strict Lyapunov conditions, and show that these reduce to LMIs when using quadratic Lyapunov certificates. Then we follow typical LMI-based characterizations of plant-order linear output feedback controller designs thus providing an optimality-based procedure for the design of the controller parameters involving a set of LMIs coupled with a line search of a few parameters. The proposed construction is illustrated on a numerical example.

Event-Triggered Fault Detection for Networked LPV Systems

This paper is concerned with the fault detection problem for a class of continuous-time linear parameter-varying systems with signal transmission delays. An effective event-triggered communication scheme is introduced to reduce the burden of the shared network where the current sampled data will be sent only when the certain condition is satisfied. By properly designing a novel fault detection filter and augmenting the states of the original system, the addressed fault detection problem can be transformed into a $$H_\infty $$ filtering problem for the filtering error system with uncertain parameters. According to the parameter-dependent Lyapunov–Krasovskii functional method and free-weighting matrix technique, the sufficient conditions, which guarantee the filtering error system satisfying the prescribed $$H_\infty $$ performance constraint, are derived in the form of parameterized linear matrix inequalities. The basic functions and gridding technique are used to deal with the corresponding parameterized convex problem. Here, the LPVTools is used to convert the infinite-dimensional feasibility conditions into a finite-dimensional set of LMIs. Then, the MATLAB LMI toolbox is applied for solving the LMI problem of finite dimensions. Moreover, the explicit expressions of the target filter parameters are also obtained. Finally, two simulation examples are provided to illustrate the validity of the proposed fault detection method.

Reliable mixed [formula omitted] and passive control for networked control systems under adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations

In this paper, the problem of reliable mixed H∞ and passive control for a class of nonlinear networked control systems under the adaptive event-triggered scheme with actuator faults and randomly occurring nonlinear perturbations is studied. Firstly, a series of independent stochastic variables with certain probabilistic distribution are presented to formulate the phenomena of actuator faults. Then, different from the traditional event-triggered scheme, the threshold of adaptive event-triggered scheme is determined by an online adaptive control law instead of the preset constant value. Further, based on a novel Lyapunov functional by taking the adaptive control law into account, sufficient conditions for asymptotically stable with mixed H∞ and passive performance are obtained in terms of a set of LMIs. If these LMIs are feasible, the reliable mixed H∞ and passive control gain and the weight parameter of adaptive event-triggered scheme can be gained simultaneously. Finally, two numerical examples are provided to show the effectiveness of the developed technique.

A Characterization of Lyapunov Inequalities for Stability of Switched Systems

We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a sufficient condition for stability. Various such conditions have been proposed in the literature in the past fifteen years. We prove in this note that a family of languagetheoretic conditions recently provided by the authors encapsulates all the possible LMI conditions, thus putting a conclusion to this research effort. As a corollary, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies stability of a switched system. Finally, we provide a geometric interpretation of these conditions, in terms of existence of an invariant set.