Observer And Controller Design For Two-dimensional Switched Linear Systems With Multiple Equilibrium Points

This thesis designs the observer and the observer-based stabilizing controller for two-dimensional switched linear systems with multiple equilibrium points.The three issues of designing the observer of two-dimensional switched linear systems with multiequilibria,the observer for two-dimensional multi-focus switched linear systems,and the observer-based region stabilizing controller are studied in the sequel.The single-input and single-output(SISO)state observer is proposed for such switched systems under arbitrary switching paths;The observer-based region stabilizing controller and its corresponding algorithm are designed for the switched systems under arbitrary periodic switching paths.The theoretical results obtained in this thesis are applied to a kind of Boost circuit to verify their practicality and effectiveness.The main contributions of this thesis are as follows.(1)The issue of designing the distributed state observers is investigated for twodimensional switched linear systems with multiple equilibrium points.Firstly,based on the basic form of Luenberger state observer,the switched error system is obtained via subtracting the system state-observer variable from the system state-observed variable.Secondly,by solving and analyzing the general solution of the switched error system,sufficient conditions of globally asymptotically stability are obtained for such switched error system;And the state observer and its algorithm are then designed for the switched systems under arbitrary switching paths.Finally,the effectiveness and practicality of the state observer and its algorithm designed in this thesis are verified via numerical simulations.(2)The issue of designing the SISO state observer is studied for two-dimensional switched linear systems with multiple focuses.Firstly,the switched error system is obtained via subtracting the system state observer variable from the system state-observed variable.Secondly,by using the common Lyapunov function method,this thesis obtains sufficient conditions of globally asymptotical stability of the switched error system,and then the system state observer together with its pseudo-code algorithm are designed for the switched systems.Finally,an illustrated numerical example is to verify the effectiveness and practicality of the obtained theoretical results.(3)The issue of designing the state observer-based region stabilizing controller is studied for two-dimensional switched linear systems with multiple focuses.At first,based on the basic form of state observer-based controller,the four-dimensional switched linear systems with multi-equilibrium points is first extended by combining the switched control systems with the switched error systems.Then,based on the region stability theory of two-dimensional switched linear systems with multiple focuses,a globally asymptotically region stabilizing controller is designed via the common region pole assignment,the coordinate transformation method and other analyzing methods,as well as an algorithm is also designed for the corresponding controller obtained.Finally,the validity and operability of the results are shown by some simulated numerical examples.(4)The issue of applying theoretical results obtained in this thesis to a kind of Boost switching circuits is studied.Firstly,by means of Kirchhoff voltage and current laws and the state space averaging method,the Boost switching circuit are formulated by a mathematical model in the form of two-dimensional switched linear systems with multiple equilibrium points.Secondly,the theoretical results given in this thesis are applied to obtain the state observer and the state observer-based region stabilizing controller for such kind of Boost circuits.Finally,the practicality and effectiveness of the obtained results are shown via numerical simulations.