Abstract -In this paper, the problem of H∞ filtering design is studied for nonlinear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. Traditionally, the sufficient conditions for the existence of such H∞ filter are characterized in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequa...

Here, we investigate boundary-value problems (BVPs) for systems of second-order, ordinary, delay-differential equations. We introduce some differential inequalities such that all solutions (and their derivatives) to a certain family of BVPs satisfy some a priori bounds. The results are then applied, in conjunction with topological arguments, to prove the existence of solutions. We then apply ea...

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This consists, given a conditional differential-algebraic system, in verifying if the system is structurally solvable for every state, and if not in finding a state in which the system is structurally singular. We give an integer linear programming formulation for the problem...

It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years, a number of integral inequalities had been established by many scholars, which are motivated by certain applications. For de...

The integral inequalities play a fundamental role in the study of existence, uniqueness, boundedness, stability, invariant manifolds, and other qualitative properties of solutions of the theory of differential and integral equations. There are a lot of papers investigating them such as [1–8]. In particular, Pachpatte [2] discovered some new integral inequalities involving functions of two varia...

The aim of this paper is to establish some new Pachpatte type inequalities on time scales, which provide explicit bounds on unknown functions. Our results extend some known Pachpatte inequalities on times scales, unify and extend some continuous inequalities and their corresponding discrete analogues. The inequalities given here can be used as tools in the qualitative theory of certain differen...

We prove instantaneous blow-up of nonnegative solutions for a class of semilinear hyperbolic inequalities with first order terms and singular coefficients. The present approach relies on a suitable choice of the functions used to test the differential inequalities.