The Bumpless Switching Control Design Of The Switching System Based On Multiple Lyapunov Functions

As a kind of special hybrid systems,switched systems are usually expressed by a set of sub-systems and switching laws.In recent decades,the analysis and design of switched systems have attracted a considerable amount of attention,such as stability analysis,L2-gain analysis,asyn-chronously switching control and fault detection problem.In practice,a switched system may not be stabilized by a single controller.It is necessary to introduce the switching control method,which requires to design different controllers for different subsystems and the switching among controllers according to the rules.However,when switching occurs,the control signal may pro-duce a big jump at the switching point,which may lead to control bumps and unexpected transient performance,even bring about negative effects on the system stability,robustness and other com-plex performance.This paper mainly studies bumpless transfer control of switched systems based on the multiple Lyapunov function method.The main contents are as follows:1)The problem of H? bumpless transfer control is investigated for switched systems under an edge-dependent average dwell time(EADT)condition.The main purpose is to find an appropriate control constraint tool for reducing the discontinuity of control signals and the influence of external interference on system performance.A global constraint is introduced to better describe the control bumps at the switching points.Considering the conservativeness of average dwell time condition,the EADT switching law is developed with more flexibilities.By using the multiple Lyapunov function method,a sufficient condition is established to solve the H? bumpless transfer control problem,which are cast into linear matrix inequalities in an easily verified form.A set of switching controllers are designed to exponentially stabilize the given system while achieving a prescribed disturbance attenuation performance.Finally,a numerical example is provided to demonstrate the effectiveness of the proposed method.2)The problem of finite-time H? bumpless transfer control is addressed for switched systems under a state-dependent condition.The main idea lies in designing a state feedback controller with amplitude limitation and a switching law to reduce control bumps caused by switching.First,a local bumpless transfer condition is proposed to limit the amplitude of switching controllers at switching points.Second,a prescribed finite-time H? performance is attained by designing a state-dependent switching law,under which the finite-time boundedness is not to be established globally for subsystems,just to be satisfied when it is activated.Then,a sufficient condition verifying the solvability of finite-time H? bumpless transfer control problem is obtained by resorting to multiple Lyapunov function method.Finally,the effectiveness of developed method is illustrated by a numerical example.3)The problem of bumpless transfer fault detection for switched systems is studied under a state-dependent condition.The main objective is to design a fault detection filter with bumpless transfer constraint and a switching law for realizing the disturbance attenuation performance of the augmented filter system,and making the residual signal more sensitive.In order to reduce control bumps,a global bumpless transfer constraint is introduced to limit the huge jumps of filters on the initial point and the switching points.Based on the multiple Lyapunov function method,a state-dependent switching law is designed with the aid of dividing the state space into a finite number of local regions,under which the fault detection performance of subsystems can be satisfied only in the local regions.Finally,the algorithm and optimization technology are applied to improve the detection effect and verify the effectiveness of the proposed method.