Iterative Linear Matrix Inequality Method Research Articles

Takagi–Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

Annulus-event-based fault detection for state-saturated nonlinear systems with time-varying delays

In this paper, the annulus-event-based fault detection method is proposed for a class of nonlinear systems subject to state saturation and time-varying delays. In particular, in order to save the network resources, a novel communication strategy called annulus-event-based triggering mechanism is considered. That is to say, the measurement output is sent to the filter only when the error between the measured value at the current moment and the data at the last transmission moment is within the prescribed triggering-annulus. Moreover, the system states at each instant are bounded by the convex hull via introducing a free matrix whose infinite norm is less than or equal to 1. Subsequently, sufficient conditions are obtained to ensure the global asymptotic stability and the H∞ performance of the filtering error dynamics system, which are expressed in line with some nonlinear matrix inequalities that can be handled via the given iterative linear matrix inequality method. Finally, two numerical simulations are employed to illustrate the validity of the developed fault detection filtering algorithm.

A proposition of iterative LMI method for static output feedback control of continuous-time LTI systems

In this paper, we propose an iterative linear matrix inequality (LMI) approach to design static output feedback (SOF) controllers for continuous-time linear time-invariant (LTI) systems. The method suggested in this paper can be viewed as a version of some previous iterative LMI methods. Although the proposed method cannot always provide improved results in comparison with the previous one, it can be used as a less conservative alternative in some cases. In addition, it can be combined with the previous algorithm to improve the results. Finally, an example is gSiven to demonstrate the validity of the proposed methods.

TLCD Parametric Optimization for the Vibration Control of Building Structures Based on Linear Matrix Inequality

Passive liquid dampers have been used to effectively reduce the dynamic response of civil infrastructures subjected to earthquakes or strong winds. The design of liquid dampers for structural vibration control involves the determination of the optimal parameters. This paper presents an optimal design methodology for tuned liquid column dampers (TLCDs) based on theH∞control theory. A practical structure, Dalian Xinghai Financial Business Building, is used to illustrate the feasibility of the optimal procedure. The model of structure is built by the finite element method and simplified to the lumped mass model. To facilitate the design of TLCDs, the TLCD parametric optimization problem is transferred to the feedback controller design problem. Through the bounded real lemma, an optimization problem with bilinear matrix inequality (BMI) constraints is constructed to design a static output feedbackH∞controller. Iterative linear matrix inequality method is employed and it added some value range constraints to solve the BMI problem. After the TLCD parameters are optimized, the responses of displacement and acceleration in frequency domain and time domain are compared for the structure with and without TLCD. It is validated that the TLCD with the optimized parameters can make the structure satisfy the need for safety and comfort.

Robust Speed Tracking of Networked PMSM Servo Systems with Uncertain Feedback Delay and Load Torque Disturbance

This paper considers a class of networked Permanent Magnet Synchronous Motors (PMSMs), whose feedback loops are closed over a shared data network. Although the installation and maintenance cost of the networked PMSM system can be lowered by replacing the conventional point‐to‐point feedback cables with a network, the network packet dropouts and transmission delay may degrade the system’s performance and even destabilize it. The load torque disturbance is another source to deteriorate the PMSM system’s performance. To investigate the effects of the data network and the torque disturbance on the speed tracking of a PMSM system is one major task of this paper. In particular, we derive a sufficient stability condition for this system in an LMI (linear matrix inequality) form and provides a way to bound the system’s H∞ performance. Moreover, we adopt an iterative LMI method to design the speed controller of the PMSM system, which can robustly guarantee stability and performance against the network‐induced delays, packet dropouts, and the torque disturbance. Simulations are done to verify the effectiveness of the obtained results.

Design of decentralized robust {ie558-1} state feedback controllerstate feedback controller

The design of decentralized robust H(subscript ∞), state feedback controller for large-scale interconnected systems with value bounded uncertainties existing in the state, control input and interconnected matrices was investigated. Based on the bounded real lemma a sufficient condition for the existence of a decentralized robust H(subscript ∞) state feedback controller was derived. This condition is expressed as the feasibility problem of a certain nonlinear matrix inequality. The controller, which makes the closed-loop large-scale system robust stable and satisfies the given H(subscript ∞), performance, is obtained by the offered homotopy iterative linear matrix inequality method. A numerical example is given to demonstrate the effectiveness of the proposed method.