The integer d is called an exponential divisor of n = ∏r i=1 p ai i > 1 if d = ∏r i=1 p ci i , where ci|ai for every 1 ≤ i ≤ r. The integers n = ∏r i=1 p ai i ,m = ∏r i=1 p bi i > 1 having the same prime factors are called exponentially coprime if (ai, bi) = 1 for every 1 ≤ i ≤ r. In this paper we investigate asymptotic properties of certain arithmetic functions involving exponential divisors a...

In a general algebraic framework, starting with a bicoprime factorization P = N,,DINpl, we obtain a right-coprime factorization N D -*, a left-coprime factorization D;’mPp, and the generalized Bezout idPen&ies associated with the pairs ( N p , 0,) and ( D p , mp). We express the set of all H-stabilizing compensators for P in the unity-feedback configuration S ( P , C) in terms of (N,,, D , N,,)...

This paper deals with design of a failure tolerant control system where failures are identified using the normalized coprime factorization method. The identification method employed is a closed-loop one, which is also based on coprime factorization; therefore, the method is suitable to the robust control systems. The impact of failure on the closed-loop stability is evaluated by ν-gap metric ob...

In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF (p)(any positive integer m) with the period 3n (n and p−1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm...

The well known state-space formulae for doubly coprime factorizations of transfer functions of stabilizable and detectable linear systems are extended to a large class of infinite-dimensional systems known as regular linear systems. Abstract-Mild sufficient conditions are given for the existence of a doubly coprime factorization of the transfer function of a regular linear system, as well as fo...

An application is presented of1 synthesis to the robust control of a large  exible space structure experimental testbed called Daisy. A perturbed left-coprime factorization of Daisy’s dynamics is used to capture the uncertainty in the modes. Designs of the 1 synthesis controller based on left-coprime factorizations of 46th-order collocated and noncollocatedmodels of Daisy are presented togethe...

Using the dual Youla parametrizations of controllerbased coprime factor plant perturbations and plant-based coprime factor controller perturbations, we study the LQG plant-controller continuity question. Indeed, we show that it is possible to calculate a new optimal LQG controller from a previous one when the plant is slightly changed, and to quantify the change in the controller as a function ...

Studies on iterative identification and model based control design have shown the necessity for identifying models on the basis of closed-loop data. Estimating models on the basis of closed-loop data requires special attention due to cross correlation of noise and input signals and the possibility to estimate unstable systems operating under a stabilizing closed-loop controller. This paper prov...

We propose a new scheme to estimate the directions-of-arrival (DOAs) of mixed coherent and uncorrelated targets exploiting a collocated multiple-input multiple-output (MIMO) radar with transmit/receive coprime arrays. In the proposed scheme, the DOAs of the uncorrelated targets are first estimated using subspace-based methods, whereas those of the coherent targets are resolved using Bayesian co...

Considering a continuous time LTI system, with impulse response hc t , the uniformly spaced samples hc nT can be identified by using an impulse train input with an arbitrarily small rate 1/NT and sampling the system output with an arbitrarily small rate 1/MT, provided M and N to be coprime for any chosen time spacing T. It is shown that different LTI filters can be identified using the sparse c...