Search for an unknown S-tuple A of significant inputs of a linear model with random IID •discrete binary carriers and finitely supported IID noise is studied. Two statistics T\ , T" s , based on maximization of Shannon Information of the joint empirical input-output distributions, are proposed inspired by the related study in Csiszar and K rner (1981). The first one compares N-sequences of teach input and of the output separately. The second one explores the relation between 5-tuples of J jV-columns of the (N X t) design matrix and the output sequence. N is the number of experiments land t is the total number of inputs. Both statistics are shown to be asymptotically as efficient as 'the ML-test based on the same two classes of joint empirical distributions in the artificial case when ML-test is applicable: if the unknown parameters 6λ, λ G A, of the model and the distribution of -errors are known. Our tests do not require this information appearing asymptotically uniformly most I efficient in the corresponding classes of tests. T s is shown to provide asymptotically the best rate of search for the set A but requires about t s log t cycles of computing. This may appear inaccessible : in some applications. T\ requires only t log t cycles of computing operations and has the rate of T the best order of magnitude. These results essentially resolve the problem of asymptotically efficient analysis of scatter diagrams posed in Random Balance Method (Budne (1959)). Results of simulation -are presented confirming theoretical results.with random jointly IID carriers Xi(X) € Β = {-1,1}, ζ* (λ) = 1 with probability /?, Ο < β < 1, λ = l, . . . , t] i = l, ... , N and IID random errors e*, i = l, . . . , N. Assume that b\ = 0 unless λ G A with cardinality \A\ = s « t. RBM was proposed Brought to you by | University of Arizona Authenticated Download Date | 6/9/15 4:52 PM M. Malyutov and H. Sadakato detect the set A ( T. A. Budne (1959)) and applied successfully to numerous cases of finding disorders of industrial production.In the discussion contained in the same issue of the journal, RBM was unanimously rejected by the leading applied statisticians of that time. They seemed to overlook the difference of the set-up studied from the estimation of parameters in (1) requiring a new type of design and analysis.Actually, the visual inspection of scatter diagrams of data TV-sequences (X N (X), Z N ) for each = 1, ...,£, was proposed by the authors of RBM, although some rank statistics (e.g. Budne test) were also applied.The main point in their arguments was probably Fisher's idea of randomization: when the value of a variable is fixed, other variables' contribution to the output is a pure noise under the random design. Hence the influence of each variable on the output can be estimated in this noisy background. It was proved in Malyutov (1979Malyutov ( , 1983 for general finitely-valued models that the asymptotic rate of ML-test is maximal for certain random designs (see below).The relevant Bahadur efficiency of linear and other rank ...

This paper considers the problem of robust stability and stabilization of uncertain time delay systems. We focus on the class of Metzlerian delay systems and use the interesting properties of Metzler matrix to provide the necessary ingredients for the main results of the paper. It is shown that Metzlerian delay system is asymptotically stable if and only if the Metzlerian system without delay* is asymptotically stable. This fact allows one to establish strong results on constrained stabilization for delay systems. The robust stability of Metzlerian delay system is also revisited and, without requiring long derivation, direct formulas for calculating the stability radius of this class of systems are provided. Finally, we consider the problem of constrained robust stabilization of interval delay systems and outline an LMI based solution for it. The paper concludes with two numerical examples to support the theoretical results.

This paper considers the problems of robust stability and stability radius pertaining to certain linear time delay systems. The aim is to establish the connection between recently published results on robust stability of time-delay systems based on matrix inequalities and computation of stability radius. As a result of this connection, an alternative formula to compute the real stability radius of time-delay systems with structured uncertainties is provided. We also report on explicit formulas for stability radius of special classes of time-delay systems.

A method for H∞ Proportional-Integral (PI) observer design for linear time-delay systems is proposed in this paper. The design method involves attenuating of the disturbance to a pre-specified level while estimating the states of the delay system. The PI observer design requires solving certain algebraic Riccati equation. Although the PI observer for time delay system is used for disturbance attenuation in this paper, it has the advantage of using it in estimating the disturbance or fault as well as other scenarios in robust control applications. The main result of the paper is the derivation of PI observer for system with one delay; however, its generalization for two delays is also outlined. Illustrative examples are included to support the theoretical results.

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