Group Of Linear Matrix Inequalities Research Articles

Fault detection for a class of nonlinear networked systems under adaptive event-triggered scheme with randomly occurring nonlinear perturbations

The problem of fault detection for a class of nonlinear systems with randomly occurring nonlinear perturbations under the adaptive event-triggered scheme is investigated. The phenomena of randomly occurring nonlinear perturbations are modelled as a stochastic variable satisfying a certain probability distribution. An adaptive event-triggered scheme is developed to further reduce the data transmission over the network and reduce the utilisation ratio of network resources. A full-order fault detection filter is constructed. By augmenting the states of the original system and the fault detection filter, the problem of fault detection is transformed into an auxiliary filtering for a time delay system. Sufficient conditions for the existence of the designed fault detection filter are obtained in terms of a group of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Absolute stability analysis of nonlinear active disturbance rejection control for electromagnetic valve actuator system via linear matrix inequality method

Nonlinear active disturbance rejection control is much more effective than linear active disturbance rejection control in tolerance to uncertainties and disturbances. However, it brings a great challenge for theoretical analysis, especially the stability analysis. This article proposes a linear matrix inequality method to analyze the absolute stability of generalized nonlinear active disturbance rejection control form which contains multiple nonlinearities with different parameters in both extended state observer and control law for single-input single-output systems. The generalized nonlinear active disturbance rejection control algorithm and the single-input single-output system are transformed into a direct multiple-input multiple-output Lurie system. A sufficient condition to determine its absolute stability based on linear matrix inequality method is given. The Lyapunov function of the Lurie system exists when the group of linear matrix inequalities is feasible. The free parameters and coefficients in Lyapunov function are given by the solution of these linear matrix inequalities. The electromagnetic valve actuator system in camless engine is presented as an application to illustrate how to perform the proposed method for absolute stability analysis and the stable region of parameter perturbations is obtained via the method. Simulation results show that the linear matrix inequality–based method is convenient and effective to determine whether the closed-loop system is absolutely stable.

A novel gain design method to improve the consensus performance of output-feedback multi-agent systems

This paper considers the consensus problem of a group of homogeneous agents. These agents are governed by a general linear system and can only directly measure the output, instead of the state. In order to achieve the consensus goal, each agent estimates its state through a Luenberger observer, exchanges its estimated state with neighbors, and constructs the control input with the estimated states of its own and neighbors. Due to the existence of observation and process noises, only practical consensus, instead of asymptotical consensus, can be achieved in such multi-agent systems. The performance of the achieved practical consensus can be measured by the ultimate mean square deviation of the states of agents. That performance is closely related to the observation gains of the state observers and the control gains of agents. This paper proposes a method to optimize such performance with respect to the concerned observation and control gains. That method starts with a set of feasible observation and control gains and formulates a group of linear matrix inequalities (LMIs). Solving these LMIs gives some intermediate matrix variables. By perturbing observation and control gains, and the intermediate matrix variables, the original LMIs yield another group of LMIs, which can be solved to provide a descent direction of observation and control gains. Moving along that descent direction, observation and control gains can be improved to yield better performance and work as the starting point of the next iteration. By iteratively repeating this procedure, we can hopefully improve the consensus performance of the concerned multi-agent system. Simulations are done to demonstrate the effectiveness of the proposed method.

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method.

Finite time takagi-sugeno fuzzy control for hydro-turbine governing system

In this study, a robust finite time Takagi-Sugeno fuzzy control method for hydro-turbine governing system (HTGS) is investigated. Firstly, the mathematical model of HTGS is introduced, and on the basis of Takagi-Sugeno (T-S) fuzzy rules, the T-S fuzzy model of HTGS is presented. Secondly, based on finite time stability theory, a novel finite time Takagi-Sugeno fuzzy control method is designed for the stability control of HTGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed finite time T-S fuzzy control scheme works well compared with the conventional method. The approach proposed in this paper is easy to implement and also provides reference for relevant hydropower systems.

Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

Decentralized finite-time H∞ filtering for interconnected Markovian jump system with interval mode-dependent delays

This paper concerns with the problem of finite-time H∞ filtering for a class of interconnected Markovian jump system with mode-dependent delays in the interconnection. Sufficient conditions guaranteeing the interconnected Markovian jump systems to be finite-time bounded are established by constructing an augmented Lyapunov–Krasovskii functional. The obtained conditions are delay-range-dependent and mode-dependent. Based on the results, the decentralized filter is proposed to guarantee the finite-time bounded and H∞ performance of the resulting augmented system for admissible disturbances. The desired filter parameters can be obtained via solving a group of linear matrix inequalities (LMIs). Finally, a numerical example is employed to illustrate the effectiveness of the proposed methods.

Robust H∞ Control for a class of Distributed Parameter Switched Systems with Neumann Boundary Conditions

The robust H∞ control for a class of distributed parameter switched systems with Neumann boundary conditions was studied. The sufficient condition of the existence of the hybrid state feedback robust H∞ controller for the closed-loop switched systems was obtained based on Green formula and Lyapunov function method. By the linear matrix inequality (LMI) approach, the design of the robust H∞ controller was converted into finding feasible solutions to a group of LMIs, which can be efficiently carried out by using Matlab LMI toolbox. Simultaneously, the method to reduce the conservativeness of the robust control system design also investigated. Finally, a numerical example shows the validity of the proposed design method.

On parameter-dependent Lyapunov functions for robust fault detection filter design with application in power systems

This study investigates the fault detection problem for uncertain linear time invariant (LTI) systems subject to polytopic uncertainties, exploiting some properties provided by the observer-based robust fault detection filter (RFDF), which has possible applications in practical power systems. By means of parameter-dependent Lyapunov functions, the existence condition of RFDF is assessed through solving a group of linear matrix inequalities (LMIs). In order to further reduce the conservativeness, an efficient algorithm in terms of LMIs by generating homogeneous polynomial parameter-dependent Lyapunov functions of arbitrary degree on the uncertain parameters is presented, which includes as special case existing conditions for RFDF design. It can be established that as the degree of the polynomial increases, the number of LMIs and free variables increases and the test becomes less conservative. Moreover, the fault sensitivity H− index can be optimized via a convex optimization algorithm, leading to the optimal RFDF. The methodology proposed can also be applied to other relevant aspects such as determining the threshold. An uncertain LTI power system model is adopted as an illustrated example to demonstrate the efficacy of the proposed methods when compared to other methods from the literature.

Characterizing the anticipating chaotic synchronization of RCL-shunted Josephson junctions

This study addresses the problem of anticipating synchronization of two chaotic RCL-shunted Josephson junctions (RCLSJ) based on time-delayed feedback control. The error dynamical system can be dealt with in virtue of non-linear pendulum-like system methods, through which we establish sufficient conditions to guarantee the existence of anticipating synchronizing slave systems. The design of a desired feedback controller can be achieved by solving a group of linear matrix inequalities (LMIs) by utilizing available numerical software. In the presence of parameter uncertainties, we further explore the robust anticipating synchronization, and propose corresponding criteria as well. These results are demonstrated through numerical simulations that under the derived conditions, the slave RCLSJ model could respond in exactly the same way as the master would do in the future, hence it allow us to anticipate the non-linear chaotic dynamics.

Takagi-Sugeno fuzzy-model-based control of hyperchaotic Chen system with norm-bounded uncertainties

In this paper, control of hyperchaotic Chen system is investigated under the existence of norm-bounded parameter uncertainties. A Takagi-Sugeno fuzzy model is employed to represent the hyperchaotic Chen system and the parallel distributed compensation technique is applied to design the time-delayed fuzzy state feedback controller. Based on Lyapunov stability theory, a sufficient delay-dependent or delay-independent stability criterion is given in term of linear matrix inequalities (LMIs) to guarantee the stability of the closed-loop system. The two sets of feedback gain matrices can be simultaneously obtained by solving a group of LMIs. Numerical simulation results demonstrate the effectiveness of the proposed method.

H∞ Model Reduction of 2-D Singular Roesser Models

This paper discusses the problem of H? model reduction for linear discrete time 2-D singular Roesser models (2-D SRM). A condition for bounded realness is established for 2-D SRM in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition for the solvability of the H? model reduction problem is obtained via a group of LMIs and a set of coupling non-convex rank constraints. An explicit parameterization of the desired reduced-order models is presented. Particularly, a simple LMI condition without rank constraints is proposed for the zeroth-order H? approximation problem. Finally, a numerical example is given to illustrate the applicability of the proposed approach.

Absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities

In this paper, necessary and sufficient conditions are obtained for the existence of Lyapunov functional of extended Lur'e form to guarantee absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities, and the existence reduces to a problem of solving a group of linear matrix inequalities (LMIs). When the LMIs are feasible, the free parameters in the Lyapunov functional are given by the solution of these LMIs. Otherwise, this class of Lyapunov functional does not exist.

A recurrent neural network for online design of robust optimal filters

A recurrent neural network is developed for robust optimal filter design. The purpose is to fill the gap between the real-time computation requirement in practice and the computational complexity of the filter design in the case that the statistical properties of noise are unknown. First, an H/sub /spl infin// requirement and an L/sub 2/ requirement of the filter design problem are formulated as a group of linear matrix inequalities. On this basis, an optimization problem is introduced to solve the robust optimal filter design problem. Then, a recurrent neural network is deliberately developed for solving the optimization problem in real time. The effectiveness and efficiency of the recurrent neural network is shown by use of theoretical and simulation results.