families of a optimal block designs for comparing test treatments with a control a optimal designs for comparing each of v test treatments simultaneously with a control in b blocks of size k each are considered it is shown that several families of bib designs in the test treatments augmented by t replications of a control in each block are a optimal in particular these designs with t 1 are optimal whenever k 2 2 1 v s k 1 2 irrespective of the number of blocks this includes bib designs associated with finite projective and euclidean geometries

optimal step type designs for comparing test treatments with a control abstract the problem of obtaining a optimal designs for comparing v test treatments with a control in b blocks of size k each is considered a condition on the parameters u b k is identified for which optimal step type designs can be obtained families of such designs are given methods of searching for highly efficient designs are proposed for situations in which it is difficult to determine an a optimal design under the usual additive homoscedastic model an a optimal design minimizes the average variance of the least squares estimators of the control test treatment comparisons majumdar and notz 1983 gave a method for finding a optimal designs their optimal designs can basically be of two types using the terminology of hedayat and majumdar 1984 rectangular r in which every block has the same number of replications of the control and step 5 in which some blocks contain the control t times and the others t 1 times optimal r type designs were studied by hedayat and majumdar 1985 f

a procedure for simultaneously stabilizing a collection of single input linear systems using non linear state feedback control abstract this paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems this stabilization is achieved using a single non linear state feedback controller the stability of the resulting closed loop system is established using a collection of quadratic lyapunov functions the main result of this paper is a sufficient condition for simultaneous stabilizability furthermore when this sufficient condition is satisfied the paper gives a formula for constructing the stabilizing feedback control law the paper includes an example in which the stabilization procedure is applied to the stabilization of an f4e fighter aircraft

discrete time asymptotic controllability implies smooth control lyapunov function we demonstrate the existence of a smooth control lyapunov function clf for difference equations asymptotically controllable to closed sets we further show that this clf may be used to construct a robust feedback stabilizer the existence of such a clf is a consequence of a more general result on the existence of weak lyapunov function under the assumption of weak asymptotic stability of a closed not necessarily compact set for a difference inclusion

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

efficient designs for comparing test treatments with a control summary the work of pearce is studied in relation to the recent research on designs for control versus test comparisons a condition for a nonorthogonal design to be most efficient is given and a lower bound to the average variance of supplemented contrasts is obtained

tight double linkage of gorenstein algebras abstract a gorenstein ideal k in a local ring r is in the class if there is a sequence of linked ideals i 0 i 1 i 2 n k with i 0 a complete intersection and i 2 i gorenstein for all i if k is in then k is linked to a complete intersection by a sequence of tight double links this means there is a sequence i 0 j 0 j 1 j 2m k such that for each p j 2 p 1 is an almost complete intersection of the form b y w and its immediate neighbors are linked to it by the similar regular sequences b y and b w respectively in this sense j 2 p and j 2 p 2 are tightly linked gorenstein ideals let k be an algebraically closed field and a k x 1 x q k with k in the k algebra a is rigid if and only if it is linked to a regular complete intersection by a sequence of semi generic tight double links it follows that if a is rigid then it is regular in codimension six

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

existence of control lyapunov functions and application to state feedback stabilizabilty of nonlinear systems the asymptotic and practical stabilization for the affine in the control nonlinear systems which extends the results of artstein sontag and tsinias is explored sufficient conditions for the existence of control lyapunov functions are presented guaranteeing stabilization the corresponding feedback laws are smooth except possibly at the equilibrium of the system

perfect linkage of cohen macaulay modules over cohen macaulay rings abstract in this paper we introduce and study the notion of linkage by perfect modules which we call perfect linkage for cohen macaulay modules over cohen macaulay local rings we explore perfect linkage in connection with syzygies maximal cohen macaulay approximations and yoshino isogawa linkage we recover a theorem of yoshino and isogawa and analyze the structure of double perfect linkage moreover we establish a criterion for two cohen macaulay modules of codimension one to be perfectly linked and apply it to the classical linkage theory for ideals we also construct various examples of linkage of modules and ideals

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

simultaneous stabilization via linear state feedback control the problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered the authors assume that the complete state can be measured and seek a static linear state feedback control law sufficient conditions for such full state gains to exist are given and they show via several examples how stabilizing compensators can be designed

simultaneous h infty control for nonlinear systems this note develops a novel method for designing simultaneous h infin state feedback controllers for a collection of single input nonlinear systems based on the kalman yakubovich popov lemma necessary and sufficient conditions for the existence of simultaneous h infin controllers are derived by the control storage function approach a universal formula for constructing continuous time invariant simultaneous h infin state feedback controllers is presented

universal formulas for feedback stabilization with respect to minkowski balls this note provides explicit algebraic stabilizing formulas for clf s when controls are restricted to certain minkowski balls in euclidean space feedbacks of this kind are known to exist by a theorem of artstein but the proof of artstein s theorem is nonconstructive the formulas are obtained from a general feedback stabilization technique and are used to construct approximation solutions to some stabilization problems

simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback the simultaneous stabilization resp asymptotic stabilization of a countable family of control systems consists of finding a control which stabilizes resp asymptotically stabilizes all the systems in the family in this paper we introduce a new method which enables us to show that given any countable family of stabilizable nonlinear systems there exists a continuous state feedback law which simultaneously stabilizes not asymptotically the family then by enriching this method we prove that any finite family of stabilizable linear time invariant lti systems can be simultaneously exponentially stabilized by means of nonlinear time varying state feedback we also derive sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of lti systems finally sufficient conditions for the simultaneous asymptotic stabilizability of finite families of nonlinear systems are provided and used for the simultaneous asymptotic stabilization of certain pairs of nonlinear homogeneous systems

simultaneous stabilization with near optimal lqr performance we consider the use of linear time varying controllers for simultaneous stabilization and performance we prove that for every finite set of plants we can design a linear time varying controller which provides not only closed loop stability but also near optimal lqr type performance by adding a mild nonlinearity in the form of a nonlinear delay we end up with an improved controller which provides near optimal performance for each possible model as well as for the case when the plant changes occasionally

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

simultaneous quadratic stabilization for discrete time nonlinear systems a constructive method is developed for designing simultaneously quadratically stabilizing state feedback controllers for a collection of single input discrete time nonlinear systems in the context of quadratic control lyapunov functions a necessary and sufficient condition for the existence of simultaneously quadratically stabilizing state feedback laws is derived an explicit formula for constructing continuous simultaneously stabilizing controllers is presented the obtained results are verified by a numerical example

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

a optimal incomplete block designs for control test treatment comparisons a optimal designs for comparing v test treatments with a control in b blocks of size k each are considered several series of a optimal designs are given when the parameters are in the range 2 k 8 k v 30 v b 50 a optimal designs in blocks of size 2 are extensively studied through a combination of theoretical results and numerical investigations tables of approximately a optimal designs are given when a optimal designs are not easily available for the case k 2

even linkage classes in this paper we generalize the s and af type resolutions used by martin deschamps and perrin for curves in ip3 to subschemes of pure codimension in projective space and shows that these resolutions are interchanged by the mapping cone procedure under a simple linkage via these resolutions rao s correspondence is extended to give a bijection between even linkage classes of subschemes of pure codimension two and stable equivalence classes of reflexive sheaves s satisfying hi 5 0 and ext1 ev 9 0 further these resolutions are used to extend the work of martin deschamps and perrin for cohen macaulay curves in 1p3 to subschemes of pure codimension two in ip in particular even linkage classes of such subschemes satisfy the lazarsfeld rao property and any minimal subscheme for an even linkage class links directly to a minimal subscheme for the dual class

licci squarefree monomial ideals generated in degree two or with deviation two abstract we study squarefree monomial ideals which are in the linkage class of a complete intersection we call such an ideal licci firstly we classify all licci edge ideals secondly we prove that any cohen macaulay almost complete intersection squarefree monomial ideal is licci thirdly we characterize licci squarefree monomial ideals of deviation 2 in terms of hypergraphs associated to the ideals as an application of the classification in kimura terai and yoshida 2009 15

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

incomplete block designs for comparing treatments wth a control general theory in this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control this class of designs is appropriate for comparing simultaneously p 2 test treatments with a control treatment the so called multiple comparisons with a control mcc problem when the observations are taken in incomplete blocks of common size k p 1 for this problem we propose a new general class of incomplete block designs that are balanced with respect to wrt test treatments we shall use the abbreviation btib to refer to such designs we study their structure and give some methods of construction a procedure for making exact joint confidence statements for this multiple comparisons problem is described by using a new concept of admissibility of designs it is shown how inferior designs can be eliminated from consideration and attention limited to a small class of btib designs that can be constructed from so called generator designs in the minimal complete class of such d

simultaneous stabilization for a collection of single input nonlinear systems this paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single input nonlinear systems the control lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time invariant simultaneously stabilizing state feedback controllers additionally a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented for any collection of second order and third order feedback linearizable systems in canonical form global simultaneous stabilization via a single state feedback controller is shown to be always possible two examples are included for illustration

robust stabilization of nonlinear systems with pointwise norm bounded uncertainties a control lyapunov function approach the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system robustly with respect to unstructured uncertainties spl phi spl tilde u x t norm bounded for each fixed x and u this condition requires one to find a smooth proper and positive definite solution v x of a suitable partial differential inequality depending only on the system data a procedure based on the knowledge of v x is outlined for constructing almost smooth robustly stabilizing controllers our approach based on lyapunov functions generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization on one hand and h sub spl infin control sector conditions and input to state stabilization on the other

optimal incomplete block designs for comparing treatments with a control abstract the problem of finding optimal incomplete block designs for comparing p test treatments with a control is studied bib designs are found to be d optimal a and e optimal designs are also obtained for a large class of functions phi conditions for a design to be phi optimal are found most of the optimal designs are certain types of btib designs introduced by bechhofer and tamhane 1981 which are binary in test treatments