We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be...We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be obtained.Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix,a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state.This condition demonstrates a method for finding the domain of attraction and its relationships.Then,all the initial states that can be stabilized are studied,and a method for designing the corresponding controller is proposed.Two examples are presented to illustrate the validity of the theoretical results.展开更多
This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive desig...This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.展开更多
This paper deals with the stabilization of the nonholonomic systems with strongly nonlinear uncertainties. The objective is to design an output feedback law such that the closed-loop system is globally asymptotically ...This paper deals with the stabilization of the nonholonomic systems with strongly nonlinear uncertainties. The objective is to design an output feedback law such that the closed-loop system is globally asymptotically regulated at the origin. The systematic strategy combines the input-state scaling technique with the backstepping technique. A novel switching control strategy based on the output measurement of the first subsystem is employed to make the subsystem far away from the origin. The simulation demonstrates the effectiveness of the proposed controller.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.61773371 and 61877036)the Natural Science Fund of Shandong Province,China(No.ZR2019MF002)。
文摘We investigate the solution and stability of continuous-time cross-dimensional linear systems(CCDLSs)with dimension bounded by V-addition and V-product.Using the integral iteration method,the solution to CCDLSs can be obtained.Based on the new algebraic expression of the solution and the Jordan decomposition method of matrix,a necessary and sufficient condition is derived for judging whether a CCDLS is asymptotically stable with a given initial state.This condition demonstrates a method for finding the domain of attraction and its relationships.Then,all the initial states that can be stabilized are studied,and a method for designing the corresponding controller is proposed.Two examples are presented to illustrate the validity of the theoretical results.
基金supported by the Research Grants Council of the Hong Kong Special Administration Region (No.412006)
文摘This paper studies the global robust stabilization problem for a class of feedforward systems that is subject to both dynamic and time-varying static uncertainties. A small gain theorem-based bottom-up recursive design is developed for constructing a nested saturation control law. At each recursion, two versions of small gain theorem with restrictions are employed to establish the global attractiveness and local stability of the closed-loop system at the equilibrium point, respectively.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 60974127.
文摘This paper deals with the stabilization of the nonholonomic systems with strongly nonlinear uncertainties. The objective is to design an output feedback law such that the closed-loop system is globally asymptotically regulated at the origin. The systematic strategy combines the input-state scaling technique with the backstepping technique. A novel switching control strategy based on the output measurement of the first subsystem is employed to make the subsystem far away from the origin. The simulation demonstrates the effectiveness of the proposed controller.
