The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singu...The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.展开更多
The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and n...The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.展开更多
In a modern power system, there is often large difference in the decay speeds of transients. This could lead to numerical problems such as heavy simulation burden and singularity when the traditional methods are used ...In a modern power system, there is often large difference in the decay speeds of transients. This could lead to numerical problems such as heavy simulation burden and singularity when the traditional methods are used to estimate the stability re- gion of such a dynamic system with saturation nonlinearities. To overcome these problems, a reduced-order method, based on the singular perturbation theory, is suggested to estimate the stability region of a singular system with saturation nonlinearities. In the reduced-order method, a low-order linear dynamic system with saturation nonlinearities is constructed to estimate the stability region of the primary high-order system so that the singularity is eliminated and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proven and the method is validated using a test power system with 3 buses and 5 machines.展开更多
This paper studies the input-output finite-time stabilization problem for time-varying linear singular sys- tems. The output and the input refer to the controlled output and the disturbance input, respectively. Two cl...This paper studies the input-output finite-time stabilization problem for time-varying linear singular sys- tems. The output and the input refer to the controlled output and the disturbance input, respectively. Two classes of dis- turbance inputs are considered, which belong to L-two and L-infinity. Sufficient conditions are firstly provided which guarantee the input-output finite-time stability. Based on this, state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable. The conditions are presented in terms of differential linear matrix inequalities. Finally, an example is presented to show the validity of the proposed results.展开更多
Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.
This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference s...This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference scheme on a uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed.展开更多
This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a unifo...This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.展开更多
Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an ...Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.展开更多
基金This work was supported by the National Creative Research Groups Science Foundation of China (No. 60421002) and the New Century 151 Talent Projectof Zhejiang Province.
文摘The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (60564001)the Program for New Century Excellent Talentsin University (NCET-06-0756)
文摘The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.
基金Supported by the National Natural Science Foundation of China (Grant No. 50595411)the New Century Outstanding Investigator Program of the Ministry of Education (Grant No. NCET-04-0529)
文摘In a modern power system, there is often large difference in the decay speeds of transients. This could lead to numerical problems such as heavy simulation burden and singularity when the traditional methods are used to estimate the stability re- gion of such a dynamic system with saturation nonlinearities. To overcome these problems, a reduced-order method, based on the singular perturbation theory, is suggested to estimate the stability region of a singular system with saturation nonlinearities. In the reduced-order method, a low-order linear dynamic system with saturation nonlinearities is constructed to estimate the stability region of the primary high-order system so that the singularity is eliminated and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proven and the method is validated using a test power system with 3 buses and 5 machines.
基金supported by the National Natural Science Foundation of China(Nos.60974137,61174141,61004005,61074070)the Research Awards Fund for Outstanding Young and Middle-Aged Scientists of Shandong Province(Nos.BS2011SF009,BS2011DX019)the Independent Innovation Foundation of Shandong University(Nos.IIFSDU2009TS085,2010TS007)
文摘This paper studies the input-output finite-time stabilization problem for time-varying linear singular sys- tems. The output and the input refer to the controlled output and the disturbance input, respectively. Two classes of dis- turbance inputs are considered, which belong to L-two and L-infinity. Sufficient conditions are firstly provided which guarantee the input-output finite-time stability. Based on this, state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable. The conditions are presented in terms of differential linear matrix inequalities. Finally, an example is presented to show the validity of the proposed results.
文摘Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.
文摘This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference scheme on a uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed.
文摘This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.
基金supported by the National Natural Science Foundation of China(61374035)
文摘Composite nonlinear feedback （CNF） control techniquefor tracking control problems is extended to the output regulationproblem of singular linear systems with input saturation. A statefeedback CNF control law and an output feedback CNF controllaw are constructed respectively for the output regulation problemof singular linear systems with input saturation. It is shown thatthe output regulation problem by CNF control is solvable underthe same solvability conditions of the output regulation problemby linear control. However, with the virtue of the CNF control, thetransient performance of the closed-loop system can be improvedby carefully designing the linear part and the nonlinear part of theCNF control law. The design procedure and the improvement ofthe transient performance of the closed-loop system are illustratedwith a numerical simulation.
