Number Of Linear Matrix Inequalities Research Articles

Fuzzy Memory Sampled-Data Controller Design for PMSG-Based WECS With Stochastic Packet Dropouts

The fuzzy memory sampled-data control problem for permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) with stochastic packet dropouts is discussed in this paper. To do this, the PMSG-based WECS dynamics are firstly modelled by a set of fuzzy IF-THEN rules of the Takagi–Sugeno (T–S) fuzzy model because of high nonlinearity. And then, to minimize design conservatism, a suitable augmented looped-type Lyapunov functional along with a novel integral inequality is established by using the sampling mode information with signal transmission delay. Further, a fuzzy memory-based sampled-data controller is designed to obtain the asymptotic stability condition under the circumstances of packet dropouts, and simultaneously, disturbance reduction is confirmed. Thereafter, the associated fuzzy controller gains can be computed by solving a number of linear matrix inequalities (LMIs). Finally, the application of the suggested method to a real-world system is proved using PMSG-based WECS, and the mathematical Rossler's system demonstrates the effectiveness and superiority of the proposed technique over the existing method.

Refined Admissible Analysis and Design Conditions for Discrete Fuzzy Singular Systems with Multiple Difference Matrices

ABSTRACT This study mainly discusses extended admissibility and fuzzy parallel distributed compensation (PDC) control issues for discrete singular fuzzy systems with multiple difference matrices existing in the rules. By the overall system associated with the discrete singular models with multiple difference matrices, we first propose an extended admissibility analysis criteria, where the new results not only involve some slack matrices but also have a less number of linear matrix inequalities’ (LMIs) constraints. Furthermore, by hiring the fuzzy PDC, explicit design criteria are further developed for the regarded system. Noticeably, the new design method can cope with controller synthesis of the admissibility and D-admissibility issues. Due to all the presented criteria are formed by the strict LMIs, we can readily evaluate them via some existing LMI solvers. Finally, two numerical examples are involved to demonstrate the applicability and the feasibility of the developed results.

Resilient sliding mode control for a class of cyber-physical systems with multiple transmission channels under denial-of-service attacks

This paper investigates the resilient sliding mode control problem for cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS) attacks. A set of finite-time observers is designed, and a switched integral-type sliding surface is introduced. Thus, the impact of unreliable state estimating channels is reduced, and the disturbance rejection performance is also improved. The number of linear matrix inequalities (LMIs) decreases compared with some existing results in designing the observer-based controller, and the input-to-state stability (ISS) is guaranteed. Moreover, the input saturation and event-triggering scheme are considered in the controller and handled by an auxiliary system. The network congestion in the control channel is thus relieved, and the Zeno behavior is excluded simultaneously. Finally, an example of an unmanned stratospheric airship is given to demonstrate effectiveness of the proposed resilient control approach.

Improved ℋ2 and ℒ2 control designs for discrete-time LPV/LFR systems

This paper addresses novel and norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to and performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples.

Mixed-sensitivity [formula omitted] controller synthesis for discrete-time LPV/LFR systems

This paper presents novel control procedure to obtain a mixed-sensitivity L2 controller for discrete-time linear parameter-varying (LPV) systems using a linear fractional representation (LFR). The proposed method makes use of parameter-dependent Lyapunov functions in combination with static full-block multipliers and slack variables to provide less conservative results than other existing control strategies. The distinctive controller is established from an observer-based control structure, where observer and state-feedback synthesis are derived. Moreover, both H2 and L2 performances indexes are addressed and some insights about factorization contractiveness are explored. The output feedback controller is given through a two-step synthesis and its design conditions are addressed in terms of a finite number of linear matrix inequalities. Finally, two numerical examples are carried out to show the effectiveness of the proposed control method.

Gain-scheduled observer-based consensus for linear parameter varying multi-agent systems

This paper investigates the gain-scheduled observer-based consensus of linear parameter varying (LPV) multi-agent systems (MASs). The main contribution of the paper is that, differently from LPV observer-based consensus design methods previously reported in the literature, the controller and observer gains are allowed to be functions of some time-varying parameter vector, which can be measured in real-time. It is shown that, under the assumption of synchronized varying parameter trajectories, the design conditions can be described as a feasibility problem involving a finite number of linear matrix inequalities (LMIs). The obtained results are illustrated by means of a numerical example.

Discrete networked dynamic systems with mode separation: state and output synchronization

This paper examines the impact of coupling in a class of linear discrete-time systems with mode separation over networks. We provide a complete analysis and design treatment allowing at extending the stabilization control design to the corresponding synchronization problem. We deploy a time-scale separation of the whole network dynamics to synthesize the controls that synchronize both the slow and fast states. We show that the design implementation is cast as feedback simultaneous stabilization framework and cast as feasibility problem over finite number of linear matrix inequalities (LMIs). As demonstrated by simulation studies, the ensuing results provide designers with a network-centric technique guarantee stability and enhance the performance of considered coupled systems.

Disturbance Observer Enhanced Neural Network LPV Control for a Blended-Wing-Body Large Aircraft

The problem of trajectory tracking control for a blended-wing-body (BWB) large aircraft with model parameter uncertainties and unknown disturbances is considered. A linear parameter-varying (LPV) model is derived from the nonlinear dynamics of the BWB aircraft from which a robust linear parameter-varying controller is designed to track a desired trajectory. Using a single quadratic Lyapunov function (SQLF) and an infinite number of linear matrix inequalities to be evaluated at all vertices, a pair of positive definite symmetric matrix solutions are determined via Lyapunov stability theory and linear matrix inequality technique. Furthermore, a disturbance-observer is designed to process the unknown disturbances. Considering the plant exists some model errors except for disturbances, a radial basis function neural network approximation is embedded into the SQLF LPV controller to improve tracking performances, and a composite disturbance-observer based neural network single quadratic Lyapunov function (NNSQLF) controller can realize desired trajectory tracking of the linear parameter-varying system through regulating performance weighting functions. The closed-loop system of trajectory tracking control is proved to be asymptotically stable by using Lyapunov theory. Simulation results of forward flight speed and altitude tracking control of the BWB aircraft show that the proposed disturbance-observer based NNSQLF control can robustly stabilize the LPV system and precisely track the desired trajectory by comparing with conventional SQLF control and parameter-dependent Lyapunov function control, even in unknown exterior disturbances and model uncertainties.

Gain-scheduled control for morphing aircraft via switching polytopic linear parameter-varying systems

This paper addresses the gain-scheduled output feedback control for morphing aircraft (MA) in full envelope using switching polytopic linear parameter-varying (SPLPV) theory. The SPLPV model of MA is derived by scheduled parameter interval division and convex decomposition. Considering average dwell time (ADT) and mode-dependent average dwell time (MDADT) switching logics, sufficient conditions to ensure that the SPLPV systems are exponential stable with weighted disturbance attenuation indexes are presented based on the multiple parameter-dependent Lyapunov functions (MPDLFs) technique, and the comprehensive algorithm for the controller solution is obtained. To reduce the computational burden and ease controller implementation, a finite number of linear matrix inequalities (LMIs) are developed for solving controller by proposing the intermediate controller variables are depend affinely on the scheduled parameter. In addition, the control matrix of linear parameter-varying (LPV) system is not limited to be constant, which greatly expands the application scope of the proposed method. The simulation validation is carried out on the SPLPV control for MA.

Observer-based control for a class of hybrid linear and nonlinear systems

An approach to output feedback control for hybrid discrete-time systems subject to uncertain mode transitions is proposed. The system dynamics may assume different modes upon the occurrence of a switching that is not directly measurable. Since the current system mode is unknown, a regulation scheme is proposed by combining a Luenberger observer to estimate the continuous state, a mode estimator, and a controller fed with the estimates of both continuous state variables and mode. The closed-loop stability is ensured under suitable conditions given in terms of linear matrix inequalities. Since complexity and conservativeness grow with the increase of the modes, we address the problem of reducing the number of linear matrix inequalities by providing more easily tractable stability conditions. Such conditions are extended to deal with systems having also Lipschitz nonlinearities and affected by disturbances. The effectiveness of the proposed approach is shown by means of simulations.

Event-based multirate control of large-scale distributed nonlinear systems subject to time-driven zero order holds

The event-based output-feedback control is studied for large-scale distributed networked nonlinear systems. All subsystems are described by interval type-2 (IT2) Takagi–Sugeno (T–S) model and communicate information to each other via distributed networks with time-varying transmission delays. The sampled rates of sensors and refresh rates of actuators are allowed to be different among subsystems. We propose an event-based control scheme in the sense that each subsystem determines its information transmission to other subsystems based on its local sampled output measurements. First, combined with the descriptor system and perturbed system approaches, an equivalent model transformation is established. Then, a relaxing Lyapunov functional is introduced by virtue of Wirtinger inequality. The corresponding co-design criteria are obtained in the form of linear matrix inequalities (LMIs), which guarantee stabilization of the closed-loop fuzzy control system with different sampling and updating rates while transmitting information via networks as little as possible. Furthermore, employing some bounding inequality techniques, a considerable reduction in the number of LMIs can be achieved. Finally, a practical application to a DC microgrid with three PV subsystems is exploited.

Stability Analysis of T–S Fuzzy Control Systems Subject to Actuator Saturation

In this paper, a stability analysis method based on a type of staircase membership functions is proposed for fuzzy control systems with actuator saturation. The staircase membership functions are used to approximate the membership functions of the fuzzy models. Due to the discreteness and finiteness of the values of staircase membership functions, the fuzzy summation inequalities describing the stability of closed-loop system can be converted to a finite number of linear matrix inequalities. The proposed method has a low degree of conservativeness since the information of membership functions is introduced into the stability analysis. Simulation results are given to show the effectiveness of the proposed methods.

Efficient LMI Conditions for Enhanced Stabilization of Discrete-Time Takagi–Sugeno Models via Delayed Nonquadratic Lyapunov Functions

This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi–Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

In this paper, a new design approach to construct a fault-tolerant controller (FTC) with fault estimation capability is proposed using a generalized Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems in the presence of actuator faults and unknown disturbances. The generalized T-S fuzzy model consists of some local models with multiplicative nonlinear terms that satisfy Lipschitz condition. Besides covering a very wide range of nonlinear systems with a smaller number of local rules in comparison with the conventional T-S fuzzy model and hence having less computational burden, the existence of the multiplicative nonlinear term solves the uncontrollability issues that the other generalized T-S fuzzy models with additive nonlinear terms dealt with. A state/fault observer designed for the considered generalized T-S fuzzy model and then, a dynamic FTC law based on the estimated fault information is proposed and sufficient design conditions are given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs are less than that of previously proposed methods and then feasibility of our method is more likely. The effectiveness of the proposed FTC approach is verified using a nonlinear mass-spring-damper system.

Stochastic stability analysis of Markovian jump linear systems with incomplete transition descriptions

In this study, the authors focus on the stability analysis for Markovian jump linear systems with partly known transition rates in the continuous-time domain and partly known transition probabilities in the discrete-time domain. By using the properties of the transition rates and transition probabilities, two new sufficient conditions are derived for the stochastic stability of the continuous-time and discrete-time Markovian jump linear systems, respectively. The main advantage of the proposed stability conditions is that the total number of linear matrix inequalities (LMIs) in the proposed stability conditions is much less than that in some existing results. Based on the presented stability conditions, two state feedback controllers are designed for the considered systems in terms of LMIs. In addition, two kinds of stability criteria are developed for the stochastic stability of the considered systems with incomplete transition descriptions by the existence of the unique positive definite solution of the coupled Lyapunov matrix equations. Finally, two numerical examples and one practical example are provided to verify the correctness of the theoretical results.

Robust sampled‐data control of non‐linear LPV systems: time‐dependent functional approach

This study addresses the problem of robust exponential stability and stabilisation of sampled-data linear parameter varying (LPV) systems with an aperiodic sampling rate. Utilising the input delay approach and taking the distance between real and measured parameters into account, new stability and stabilisation conditions are derived for LPV systems with arbitrary dependence on the parameters. By means of a modified parameter dependent Lyapunov-Krasovskii functional, stability conditions are formulated as a set of parameter-dependent linear matrix inequalities (PLMIs) which are suitable to investigate the effect of the sampling rate on the closed-loop stability. Furthermore, sufficient conditions to guarantee the feasibility of PLMIs over the set of whole parameters are derived that lead to the feasibility of a finite number of linear matrix inequalities. Applying the projection lemma new stability analysis conditions are obtained and shown to be suitable for the stabilisation problem. Under the new stability criteria, an efficient procedure developed for robust sampled-data controller design in the presence of uncertainty on the varying parameters and unknown time varying sampling rate. The proposed method is applied to a sampled-data fuzzy control problem of a non-linear system and multi-rate sampled-data LPV systems. Several examples show the efficiency of the method.

Robust dynamic surface control of vehicle lateral dynamics using disturbance estimation

This paper reports a disturbance estimation-based dynamic surface control method for stabilizing vehicle lateral dynamics through yaw moment control. Based on the single track vehicle model, an uncertain model of the vehicle lateral dynamics is developed which represents the effect of parametric uncertainty and lateral tire force nonlinearity by mismatched, lumped total disturbances. In this model, the longitudinal velocity of the vehicle is considered as a time-varying parameter. Using the developed mathematical vehicle model, an extended state observer is proposed to estimate the total disturbance signals. Next, a dynamic surface controller is designed with the objective of tracking the desired lateral velocity generated by a linear two-degrees-of-freedom vehicle dynamics. The dynamic surface controller uses the estimated disturbances of the extended state observer as feedforward inputs to compensate for the effects of the total disturbances. To achieve an improved robust performance against disturbance estimation errors, the [Formula: see text] control technique is incorporated into the DSC design. To this end, using a norm-bounded representation of the longitudinal velocity, the control design is formulated as the feasibility of a finite number of linear matrix inequalities. The stability and robustness of the extended state observer and the dynamic surface control systems are analyzed in a Lyapunov framework and the required mathematical proofs are presented. Considering a lane change and a J-turn maneuver, extensive numerical simulations are performed to show the effectiveness of the proposed control system. The results confirm the improved performance of the closed-loop system compared to the open-loop one, in various driving and road conditions.

New Stability Criterion for Continuous-Time Takagi-Sugeno Fuzzy Systems With Time-Varying Delay.

In this technical paper, a new Lyapunov-Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi-Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time t which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.

Energy-to-peak consensus for multi-agent systems with stochastic disturbances and Markovian switching topologies

This paper is concerned with the problem of energy-to-peak consensus for a class of multi-agent systems with both stochastic disturbances and Markovian switching topologies. The objective is to design a control protocol in the form of dynamic output feedback, such that the multi-agent system reaches mean square consensus and has a prescribed energy-to-peak disturbance attenuation level. By using linear transformations, the problem is transformed into a standard energy-to-peak control problem. Then a new bounded real lemma is established. On the basis of this, an approach for the design of the control protocol is developed, by which the desired gain can be obtained via solving a number of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Reducing the number of vertices in some Takagi-Sugeno models: example in the mechanical field

This paper is concerned with the building of application-oriented model-based Takagi-Sugeno models that arise from sector nonlinearity methodology. Despite its exactness, this modeling technique produces a polytopic embedding with a number of vertices of 2 raised to the number of nonlinearities which, if high, represents a rapid growth in the number of linear matrix inequalities (needed to solve even the simplest control and observation schemes). A solution for model reduction is proposed based on the similarity of Taylor approximations amongst nonlinearities, with a measurable bound on the approximation, which - as proven with a suitable application example - brings the methodology closer to real-time demands.