This paper analyzes several properties linked to the robust control of fractional diier-ential systems with delays. The BIBO stability of both retarded and neutral fractional delay systems is characterized in terms of the location of their poles. In the particular case of retarded systems, we give some properties of the poles of the system and the singular values of its Hankel operator, as well...

This paper investigates the L-stability properties of fractional nonlinear differential equations. Systems defined on a finite time interval are considered. The principal contributions are summarized in a theorem which give sufficient conditions for bounded stability of fractional order systems. We show that the proposed results can not be extended to the case of systems defined on an infinite ...

We consider the large deviations properties of the empirical measure for one dimensional constrained processes, such as reflecting Brownian motion, the M/M/1 queue, and discrete time analogues. Because these processes do not satisfy the strong stability assumptions that are usually assumed when studying the empirical measure, there is significant probability (from the perspective of large devia...

We consider the aggregation equation ut = ∇·(∇u−u∇K(u)) in a bounded domain Ω ⊂ R with supplemented the Neumann boundary condition and with a nonnegative, integrable initial datum. Here, K = K(u) is an integral operator. We study the local and global existence of solutions and we derive conditions which lead us to either the stability or instability of constant solutions.

This paper deals with the determination of the conditions for which the hysteretic Bouc-Wen model is consistent with the physical phenomenon it is supposed to represent. In particular, we derive the conditions on the model parameters under which the model is stable, asymptotically dissipative and verifies the hysteretic property. These conditions are in the form of algebraic inequalities to be ...

Stability issues of linear Takagi–Sugeno (T–S) fuzzy models are investigated. We first propose a systematic way of searching for a common matrix, which, in turn, is related to stability for N subsystems that are under a pairwise commutative assumption. The robustness issue under uncertainty in each subsystem is then considered. We then show that the pairwise commutative assumption can, in fact,...

We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such programs is based on linear algebraic methods. We reduce the verification of the termination problem to checking the orthogonality of a well determined vector sp...

We prove the global asymptotic stability of a well-known delayed negativefeedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length.

The directed search model (Peters, 1984) is static; its dynamic extensions typically restrict strategies, often assuming price or match commitments. We lift such restrictions to study equilibrium when search can be directed over time, without constraints and at no cost. In equilibrium trade frictions arise endogenously, and price commitments, if they do exist, are self-enforcing. In contrast to...

For symmetric indeenite tridiagonal matrices, block LDL T factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots.