Abstract: Stability analysis and stabilization synthesis problems of the singularly perturbed switched systems (SPSSs) are investigated in this paper. First, stability of the SPSS with stable subsystems is discussed by using an average dwell time approach with a full-order piecewise Lyapunov function. Then, the result is extended to the situation that not all the subsystems are Hurwitz stable. ...

Using Brouwer degree, we prove a more general version of the zero exclusion principle for families of polynomials and apply it to obtain very simple proofs of extensions of recent results on the Routh-Hurwitz and Schur-Cohn stability of families of polynomials. 1. Introduction It is well know that the problem of the stability of a linear diierence or differential system with constant coeecients...

An extension of Kato’s stability condition for nonautonomous Cauchy problems is presented. It is proved that in the commutative case this condition and a mild regularity assumption imply wellposedness. If one supposes the Kato-stability, then the solutions are given by an integral formula. By means of examples we show that in general these stability conditions cannot be omitted in our results. ...

The aim of this paper is to give sufficient conditions for a switched linear system defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function to be GUAS. We show that this property is equivalent to the uniform observability on [0,+∞) of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switc...

Necessary and sufficient conditions for the bi-variate characteristic polynomial of a matrix to be very strict Hurwitz (VSHP) are presented. These conditions are based on solving the Lyapunov equation for 2 0 continuous systems using the Kronecker product and lead to a simple test for the VSHP property. It requires testing only the eigenvalues of three stable matrices and this is simpler than t...

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua’s circuits can be achieved by using the second state as feedba...

1.1. Log-K-stability Let (X, J) be a Fano manifold, that is, K−1 X is ample. A basic problem in Kähler geometry is to determine whether (X, J) has a Kähler–Einstein metric (see [22]). The existence problem of Kähler–Einstein metric is a special case of the existence problem of constant scalar curvature Kähler (cscK) metric. For the latter, we fix an ample line bundle L on (X, J). We have the fo...

Abstract. We establish a series of indefinite integral formulae involving the Hurwitz zeta function and other elementary and special functions related to it, such as the Bernoulli polynomials, ln sin(πq), ln Γ(q) and the polygamma functions. Many of the results are most conveniently formulated in terms of a family of functions Ak(q) := kζ (1 − k, q), k ∈ N, and a family of polygamma functions o...

The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical de nite integral due to Euler and other de nite integrals are also considered together with closed-form evaluations of some series involving the Riemann and Hurwitz Zeta functions.

Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...