ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS

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.

Kamenev-type Oscillation Criteria for Semilinear Elliptic Differential Equations

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.

Non-fragile decentralized H_∞ controller design for uncertain linear systems

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.

Oscillation Criteria Related to Integral Averaging Technique for Quasilinear Elliptic Equations

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.

On common solutions of Riccati inequalities

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.

OSCILLATION CRITERIA FOR NONLINEAR SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

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.