This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater detail. In the current paper, for homogeneous networks with time-invariant interconnection dynamics, it is illustrated how the zeros of each individual agent’s...

Al~lract--Motivated by a crucial role blocking zeros play in deciphering the strong stabilizability of a given system, a careful study of blocking zeros is undertaken here. After developing certain properties of blocking zeros and based on the multiplicity structure of invariant zeros, we identify what kind of invariant zeros are blocking zeros. For controllable and observable systems, an invar...

This paper introduces integral resonant control, IRC, a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. By adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. It is shown that this...

A simple controller synthesis method is developed for certain classes of linear, time-invariant, multiinput multi-output plants. The number of poles in each entry of these controllers depends on the number of right-half plane plant zeros, and is independent of the number of poles of the plant to be stabilized. Furthermore, these controllers have integral-action so that they achieve asymptotic t...

Let D be a real function such that D(z) is analytic and D(z) ± 0 for \z\ < 1. Furthermore, put W(x) = \J\ x2\D(e'v)\2 , x = costp , tp e [0, 71 ], and denote by pn(', rV) the polynomial which is orthogonal on [-1, +1] to Pn_[ (P„_! denotes the set of polynomials of degree at most n 1 ) with respect to W . In this paper it is shown that for each sufficiently large n the polynomial En+X(-, W) (ca...

which is valid for any complex s, it follows that ζ(s) has zeros at s = −2,−4, . . . . These zeros are called the “trivial” zeros of ζ(s), to distinguish them from the complex zeros of ζ(s). The zeta-function has also an infinity of complex zeros. It is well-known that all complex zeros of ζ(s) lie in the so-called “critical strip” 0 < σ = R s < 1, and if N(T ) denotes the number of zeros ρ = β...

One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...

We discuss the relationship between the large order behavior of the perturbative series for the average plaquette in pure gauge theory and singularities in the complex coupling plane. We discuss simple extrapolations of the large order for this series. We point out that when these extrapolated series are subtracted from the Monte Carlo data, one obtains (naive) estimates of the gluon condensate...

The Assignment algorithm is around 54 years old and a lot of work has been done on this algorithm. In this study various aspect of assignment algorithm has been considered. The endeavor of this note is to make solution of assignment problem so simple that even class tenth student can easily solve it. One of the most important aspects of assignment algorithm (Hungarian Algorithm) is to draw line...

We present a Non-relativistic Quantum mechanical model, which exhibits the realization of Riemann Conjecture. The technique depends on exposing the S-wave Jost function at zero energy and in identifying it with the Riemann ξ(s) function following a seminal paper of N. N. Khuri. ∗I dedicate this note to my teacher, George Sudarshan of the University of Texas at Austin We begin by recalling the a...