Control Design For Switched Singular Systems With State Jumps

Switched systems,as a special class of complex systems,have received increasing attention in the last few decades.When all or part of the subsystems of a switched system are subject to algebraic constraints,a broader class of switched singular systems are constituted,the complex structures and special switching rules make them widely available in practical engineering systems,such as power circuit systems,economic systems,robotic systems,flight control systems and so on.Almost all systems in industrial production are nonlinear and contain uncertainty disturbances due to the complex environment,which brings great challenges to the study of control systems.With the rapid development of digital technology,more and more digital devices are used in control systems.The traditional time-triggered sampling has a simple structure but a large amount of redundant sampling information will occupy the limited bandwidth and cause a waste of resources.Thus,event-triggered control has received increasing attention.In addition,the current research on the switched singular system mainly focuses on the steady-state performance,while little attention is paid to the transient performance,especially the superposition effect of sampling and switching control will further enhance the effect of state jumps and control input bumps.Such discontinuous transient characteristics often have a negative impact on the system,which may lead to serious performance degradation and even to system instability.This dissertation uses the continuous-time switched singular systems as models to discuss the control problem for the switched singular system with state jumps,including the event-triggered control problem affected by asynchronous switching,event-triggered H∞ control for the nonlinear switched singular system,event-triggered bumpless transfer control problem to suppress the signal bumpy behavior,and the anti-disturbance problem based on the uncertainty and disturbance estimator.The main contents of this dissertation include the following six chapters:In Chapter 1,the research background and motivation of this dissertation are introduced,and the current status of research on switched systems,switched singular systems,anti-disturbance control,and event-triggered control are reviewed from different perspectives.Some necessary lemmas and definitions are given,the works and innovations in the dissertation are summarized.In Chapter 2,the event-triggered control problem for switched singular systems with asynchronous switching and state jumps is studied.To describe the instantaneous state jumps caused by the switching law and different algebraic constraints,an improved consistency projection operator is proposed.By constructing a multiLyapunov function,several sufficient conditions are given to guarantee the regularity,impulselessness,and globally uniformly exponential stability of the closed-loop system under event-triggered state-feedback control.The observer-based stability conditions are reformulated by constructing a Luenberger-like observer to estimate the continuous and jump states,and the design of the event-triggered controller and observer are given by transforming the above bilinear matrix inequality conditions into linear matrix inequalities(LMIs)conditions using matrix decoupling techniques.Additionally,Zeno behavior is excluded by calculating a lower bound on the event-triggered sampling interval.Finally,the validity of the results in this chapter is verified by two numerical examples and the servo motor application.In Chapter 3,the composite event-triggered H∞ control problem for nonlinear switched singular systems with mode-dependent event-triggering strategies is investigated.Due to the effects of nonlinearity and unknown input disturbances,the switching-induced state jumps are difficult to describe using the consistency projection operator in Chapter 2,thus,a composite controller consisting of a state feedback controller and a impulsive controller is designed,where the impulsive control is introduced to transform the nonlinear switched singular system into an impulsive nonlinear switched singular system.Moreover,a mode-dependent hybrid triggering strategy is constructed to overcome Zeno behavior and the asynchronous phenomena caused by the event triggering.Based on the admissible edge-dependent average dwell time method,several sufficient conditions are given to ensure that the closed-loop system is regular,impulse-free,has a unique solution,is globally uniformly asymptotically stable with a weighted H∞ performance,the design method of the controller is also given.Furthermore,it is verified numerically that Zeno behavior can be excluded under the proposed event-triggering strategy.Finally,a numerical example and a circuit model with nonlinear resistances are given to illustrate the effectiveness of the methods in this chapter.In Chapter 4,the event-triggered bumpless transfer control problem for nonlinear switched singular systems with state jumps is investigated.In order to quantify the amplitude of state jumps and control input jumps,two new definitions of bumpless transfer performance are proposed.Since the states of the system are unavailable,an improved circle criterion-based observer is used to estimate the unknown states,and an observer-based mode-dependent hybrid event-triggering strategy is proposed to improve efficiency and save resources.An observer-based event-triggered bumpless transfer control strategy is proposed and jointly designed with an event-triggered scheme to quantify the amplitude of control input jumps and state jumps.Such a control scheme can achieve a balance between steady-state and transient performance.Combined with the mode-dependent average dwell time approach,sufficient conditions are given to ensure that the closed-loop system is regular,impulse-free,has a unique solution,is globally uniformly asymptotically stable with event-triggered bumpless transfer performance,and the controller is designed.In addition,Zeno behavior is excluded from a numerical point of view by calculating the lower bound of the event-triggered sampling interval.Finally,a numerical example is given to illustrate the effectiveness of the methods in this chapter.In Chapter 5,the input-to-state stability problem for impulsive switched singular systems with mismatched disturbances is considered.The term ’disturbance’ in this chapter is a general concept that includes uncertain parameters,nonlinear perturbations,external disturbances and so forth.The core idea of this chapter is to offset the effect of mismatched disturbances by introducing a virtual input,then input-to-state stability for single singular system and impulsive switched singular systems is investigated by an improved UDE-based control method.Several linear matrix inequality conditions are given to ensure the stability of the closed-loop systems under the admissible edge-dependent average dwell time method,and the design method of controller is also given.Finally,two numerical examples are reported to verify the effectiveness of the methods of this chapter.In Chapter 6,the main contributions are summarized and further research is envisioned for the future.