This paper studies a method of shifting poles of linear constant systems via LQ optimal feedback. By making use of a solution to the so-called inverse regulator problem, this method enables us to shift poles successively by pairs while maintaining the well-known advantages of LQ regulators. Polynomial fractional representation is effectively used both to characterize the maximal pole-assignable...

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

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We develop a higher-order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the multilinear normal model. This role is analogous to that of the LQ decomposition in likelihood inference for the multivariate normal model. Additionally, this hi...

The performance of the linear consensus algorithm is studied by using a Linear Quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting an analogy between Markov Chains and electrical resistive networks. Indeed, this permits to uncover the relation between the LQ performance cost and the average effective resist...

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Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let...

Let L(ν)⊗̂γqY = Lq(ν, Y ) and X⊗̂∆pL(μ) = Lp(μ,X). It is shown that any Lp(μ)-valued measure has finite L2(ν)-semivariation with respect to the tensor norm L(ν)⊗̂∆pL(μ) for 1 ≤ p < ∞ and finite Lq(ν)semivariation with respect to the tensor norm L(ν)⊗̂γqL(μ) whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor no...