Oscillation criteria for semilinear elliptic differential equations are obtained. The results are extensions of integral averaging technique of Kamenev. General means are employed to establish our results.
Sufficient conditions are obtained for oscillation of certain quasilinear elliptic equations div(｜Du｜m-2A（x）Du)+p（x）｜u｜m-2u=0, x∈ΩRn, where Ω is an exterior domain, m>1, and p（x） is an alternating func...Sufficient conditions are obtained for oscillation of certain quasilinear elliptic equations div(｜Du｜m-2A（x）Du)+p（x）｜u｜m-2u=0, x∈ΩRn, where Ω is an exterior domain, m>1, and p（x） is an alternating function. The integral averaging technique is employed to establish our results.展开更多
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ...By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.展开更多
Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The par...Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.展开更多
This paper extends the previous work on common positive definite solutions (CPDSs) to planar algebraic Riccati inequalities (ARIs) to those with arbitrary dimensions.The topological structure of the set of all positiv...This paper extends the previous work on common positive definite solutions (CPDSs) to planar algebraic Riccati inequalities (ARIs) to those with arbitrary dimensions.The topological structure of the set of all positive definite solutions of an ARI is investigated.This leads to a necessary and sufficient condition for the existence of CPDSs to a set of Riccati inequalities.It also reveals that the solution set of ARIs is a positive cube in Rn,which arouses a new method to search the CPDS.Some examples of three-dimensional ARIs are presented to show the effectiveness of the proposed methods.Unlike linear matrix inequality (LMI) method,the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.展开更多
The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are establi...The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.展开更多
文摘Oscillation criteria for semilinear elliptic differential equations are obtained. The results are extensions of integral averaging technique of Kamenev. General means are employed to establish our results.
文摘Sufficient conditions are obtained for oscillation of certain quasilinear elliptic equations div(｜Du｜m-2A（x）Du)+p（x）｜u｜m-2u=0, x∈ΩRn, where Ω is an exterior domain, m>1, and p（x） is an alternating function. The integral averaging technique is employed to establish our results.
文摘By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory.
基金the National Natural Science Foundation of China (60674019).
文摘Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministryby the Aerospace Science Foundation of China (No. 2009ZH68022)the Program of 985 Innovation Engineering on Information at Xiamen University(2009-2011)
文摘This paper extends the previous work on common positive definite solutions (CPDSs) to planar algebraic Riccati inequalities (ARIs) to those with arbitrary dimensions.The topological structure of the set of all positive definite solutions of an ARI is investigated.This leads to a necessary and sufficient condition for the existence of CPDSs to a set of Riccati inequalities.It also reveals that the solution set of ARIs is a positive cube in Rn,which arouses a new method to search the CPDS.Some examples of three-dimensional ARIs are presented to show the effectiveness of the proposed methods.Unlike linear matrix inequality (LMI) method,the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.
文摘The second order elliptic differential equations are considered in an exterior domain Ω Rn, n≥2, where p can chang sign. Some new sufficient conditions for the oscillation of solutions of (1.1) and (1.2) are established.
