Stabilization of Large-Scale Fuzzy Interconnected System

The chapter addresses the stabilization problem for large-scale fuzzy interconnected systems. Our aim is to present the design results on both the state feedback and static-output feedback (SOF) stabilizing fuzzy controllers. Firstly, by using some bounding techniques, the reduced number of LMIs to the decentralized state feedback controller design will be derived. Then, by using some matrix transformation techniques and singular system approach, we will also derive some design results on decentralized SOF control in terms of LMIs. Moreover, the proposed design results on the decentralized control will be extended to address the distributed control problem. Finally, several examples are given to illustrate the use of corresponding results.

Sliding-Mode Control of Large-Scale Fuzzy Interconnected Systems

This chapter will study the decentralized SMC for large-scale fuzzy interconnected systems. The design result on the decentralized sliding mode control of the continuous-time systems is derived in terms of LMIs. We also extend the result to discrete-time systems. Two simulation examples are provided to validate the advantage of the proposed methods.

Event-Triggered Control of Large-Scale Fuzzy Interconnected Systems

This chapter studies the event-triggered control problem for large-scale networked fuzzy systems with transmission delays and nonlinear interconnections. Our considered scheme is decentralized event-triggered control in the sense that each subsystem is able to make broadcast decisions by using its locally sampled data when a prescribed event is triggered. We propose two different approaches to solve the co-design problem consisting of the controller gains, sampled period, network delay, and event-triggered parameter in terms of a set of LMIs. Also, we consider a self-triggered control scheme in which the next triggered time is precomputed. Finally, two simulation examples are provided to validate the advantage of the proposed methods.

Practical Application

In this chapter, we pay our attention to the two practical applications (Microgrid and Multi-Motors driven) for the proposed methods.

Sampled-Data Control of Large-Scale Fuzzy Interconnected Systems

This chapter aims to study the sampled-data stabilization for large-scale fuzzy interconnected systems. We use two approaches to design the decentralized fuzzy sampled-data controller: Wirtinger's inequality and scaled small gain (SSG) theorem. Our aim is to derive the co-design consisting of the controller gains and sampled period in terms of a set of LMIs. Also, we consider the distributed sampled-data control problem, where the sampling periods among all subsystems may be different, and the actuator in each subsystem is time-driven. Finally, two simulation examples are provided to validate the advantage of the proposed methods.

Stability of Large-Scale Fuzzy Interconnected System

This chapter studies the asymptotic stability of large-scale fuzzy interconnected systems. It firstly focused on the general stability analysis. Then, by using some bounding techniques, the fuzzy rules in interconnections to other subsystems are eliminated. Such condition leads to a reduced number of LMIs. Also, we will present the stability result for the discrete-time case. Finally, we give several examples to illustrate the use of corresponding results.

Introduction

The book presents a foundational and comprehensive treatment of the analysis and design tasks for large-scale nonlinear interconnected systems based on the Takagi-Sugeno (T-S) model. Expect stability analysis, an emphasis is laid on the derivation of methods which have a decentralized or a distributed control structure. These include sampled-data control, event-triggered control, sliding mode control, practical applications, and last but not the least, conclusions and future research. The proposed methodologies provide effective techniques to overcome specific difficulties in the considered systems, such as high dimensionality, interconnections, and coupling nonlinearities.

Conclusions and Recommendations for Further Research of Large-Scale Fuzzy Interconnected Control Systems

In this chapter, our purpose hereafter is to shed more light on some prevailing aspects and potential remarks in the fuzzy control of large-scale fuzzy interconnected systems from fuzzy modeling and analysis aspects, control aspects, application aspects, and future research.