stabilisation using a stable controller and robust stability and performance a class of strictly proper multi input multi output mimo causal linear time invariant lti systems with a detectable and stabilisable realisation in a proposed observer controller scheme is considered this class is characterised by the rank of the observability matrix in closed loop the considered scheme is based on an pre compensator and on an dual post compensator stabilising a full actuation full information plant and on pseudo inverses of the input and of the output matrices the pre compensator and post compensator are of reduced complexity and belong to the family of all stabilising controllers the separation principle is satisfied and necessary and sufficient stability conditions are presented for the overall system getting a stable controller an algebraic approach and a state space approach are used to find this stability condition the estimated error is zero in stationary state also the control parameters allow the stationary state error and the complementary sensitivity funct

on the order of stable compensators abstract by means of two typical examples it is shown that in general the minimal order of a stabilizing stable compensator may not be bounded in terms of the plant order such bounds can only be given in the special case of plants with at most one right half plane zero implications for the simultaneous stabilization problem are elucidated

implementation of a maximin power clustering criterion to select near replicates for regression lack of fit tests abstract in earlier work we presented a maximin power clustering criterion to partition observations into groups of near replicates specifically the criterion selects near replicate clusters for use with christensen s tests for orthogonal between and within cluster lack of fit this article further explores implementation of this clustering criterion in particular a methodology is developed to determine a collection of candidate groupings to which the maximin power criterion can be applied

brief paper strong γk γclh stabilization with a new slack variable approach this paper deals with the strong c email protected c lh stabilization problem a new bounded real lemma is provided by adding two slack variables which provides extra freedom to include more control constraints in handling robust control problems with the extended bounded real lemma a new sufficient condition is proposed for nth order strong c email protected c lh stabilization it is also proved that the design of an lxnth order l 2 strong c email protected c lh controller can be transformed into that of an nth order controller for an associated plant which tackles the possible order problem furthermore the h stable stabilization and strong stabilization problems can also be solved by relaxing certain constraints accordingly despite the bmi constraints the path following and alternative iteration methods are adopted to propose procedures for both nth and lxnth order controller designs the effectiveness is indicated by several numerical examples

low order integral action controller synthesis abstract a simple controller synthesis method is developed for certain classes of linear time invariant multi input 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 tracking of step input references with zero steady state error the designed controller s poles and zeros are all in the stable region with the exception of one pole at the origin for the integral action design requirement the freedom available in the design parameters may be used for additional performance objectives although the only goal here is stabilization and tracking of constant references

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

brief a parametric optimization approach to h and h2 strong stabilization this paper presents an approach for designing stable mimo h and h 2 controllers by directly computing the norm constrained stable transfer matrices q in the h and h 2 suboptimal controller parameterizations this is done by first converting the h 2 and h strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parameterization of the norm constrained q s for any fixed order then a two stage numerical search is carried out by using a combination of a genetic algorithm and a quasi newton algorithm in order to reach an optimal solution the effectiveness of the proposed algorithms is illustrated through some benchmark numerical examples

frequency weighted controller reduction methods and loop transfer recovery abstract this paper shows that if one designs an lqg controller using the conventional technique of loop transfer recovery ltr then two frequency weighted controller reduction methods the enns frequency weighted balanced truncation enns 1984a ph d thesis stanford university ca 1984b proc 23rd cdc las vegas nv 127 132 and the bezout identity induced frequency weighted reduction method anderson and liu 1987 proc amer control conf mn will be equivalent under the condition that the plant transfer function is square nonsingular and minimum phase we also show that enns method is equivalent to the bezout identity induced frequency weighted reduction method if the controller itself is stable and a particular representation for the controller is assumed

properties of optimal weighted sensitivity designs weighted sensitivity designs for a class of single input single output linear time invariant systems are shown to have the property that the optimal controller has fewer right half plane poles than the plant has right half plane zeros while weighted complementary sensitivity designs are shown to have the property that the optimal controller has fewer right half plane zeros than the plant has right half plane poles effects of various choices of weighting functions on the optimal solutions are described

maximin clusters for near replicate regression lack of fit tests to assess the adequacy of a nonreplicated linear regression model christensen introduced the concepts of orthogonal between and within cluster lack of fit with corresponding optimal tests however the properties of these tests depend on the choice of near replicate clusters in this paper a graph theoretic framework is presented to represent candidate clusterings a clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a specified graph on the predictor settings examples are given to illustrate the methodology

some new results on strong gamma_k gamma_ cl h_ infty stabilization the strong gammak gammacl hinfin stabilization problem is addressed in this paper based on the bounded real lemma an improved sufficient condition on strong hinfin stabilization as well as its dual form is derived which extends the are constraint in the former results into an inequality constraint two path following algorithms are proposed to solve the associated optimization problems with bmi constraints which lead to full order controllers a numerical example is presented to demonstrate the effectiveness of the result

on the stable spl hscr sub spl infin controller parameterization under sufficient condition suboptimal spl hscr sub spl infin controller is said to internally stabilize the closed loop transfer matrix however the stability of the controller is not assured in the conventional spl hscr sub spl infin control theory an unstable controller can damage the whole system when the sensor fails or actuator saturates this paper presents a stable n dimensional spl hscr sub spl infin controller and its parameterization for the lti system based on the sufficient condition for the existence of a stable spl hscr sub spl infin controller the stability of spl hscr sub spl infin controller and closed loop transfer matrix is guaranteed if the positive semidefinite solutions for the suggested three riccati equations exist

design of a minimal precompensator for the decoupling problem abstract for right invertible linear time invariant systems which cannot be decoupled row by row using regular static state feedback laws we propose a new algorithmic procedure for designing a minimal precompensator leading to a compensated system which can be decoupled by regular static state feedback

decoupling with internal stability for unity output feedback systems abstract this paper presents for the first time a necessary and sufficient condition for solvability of the decoupling problem with internal stability for square plants by unit output feedback compensation it consists of some polynomial matrix coprimeness conditions and is concerned only with the greatest c divisor of the plant parameterizations of all decoupling compensators and achievable diagonal loop maps with internal stabilizability are given and the results are also generalized in a very natural way to the decoupling problem with arbitrary pole assignment examples are included for illustration

a unifying approach to the decoupling of linear multivariate systems a unifying approach to the decoupling problem diagonal triangular block decoupling is introduced the key element is the interactor a polynomial matrix of unique structure associated with the transfer matrix of the system necessary and sufficient conditions for block decoupling are derived and the stability questions are resolved using the block coupling zeros the results obtained for decoupling via state feedback state feedback plus input dynamics and constant output feedback are conceptually simple unify and expand those existing and easily lead to constructive decoupling algorithms

solvability of the decoupling problem for linear constant a b c d quadruples with regular output feedback the aim of this paper is to deal with the general decoupling problem of linear constant a b c d quadruples under the assumption of regular output feedback in its most general setting this problem was hitherto unsolved here we give a complete characterization of solutions by regular output feedback by means of necessary and sufficient conditions of existence they generalize the result previously obtained by denham 4 for the linear constant a b c triples

design of stable controllers attaining low h sup infinity weighted sensitivity strong stabilization and sensitivity reduction for a linear time invariant single input single output system are considered stable controllers are practically desirable in the presence of possible actuator or sensor failures it is verified precisely that the optimal controller of h sup infinity weighted sensitivity minimization is almost always unstable when the plant has more than two zeros in the right half plane an algorithm for attaining the low sensitivity property for stable controllers is presented it is based on nevanlinna pick interpolation

on the order of simultaneously stabilizing compensators in this paper simultaneous strong stabilization problem is considered and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator in terms of the plant orders a similar problem was also considered by smith et al 1986 where it was shown that such a bound does not exist for the strong stabilization problem of a single plant but the examples given in the article were forcing an approximate unstable pole zero cancellation or forcing the distance between two distinct unstable zeros to go to zero in this paper it is shown that 1 if approximate unstable pole zero cancellation does not occur and the distances between distinct unstable zeros are bounded below by a positive constant then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator and 2 for the simultaneous strong stabilization problem even for the two plant case such a bound cannot be found

linear feedback decoupling transfer function analysis the problem of linear system decoupling is examined based on recent results on linear feedback new insight is obtained through which resolution of the decoupliug problem is accomplished by calculations performed directly on the given transfer matrix computation of the decoupling compensators follows by easy constructions the problem of feedback block decoupling with internal stability is also formulated and resolved

feedback block decoupling and infinite structure of linear systems abstract using factorizations at infinity of the transfer matrix two interesting necessary and sufficient conditions arc obtained for the block decoupling problem of linear systems by state feedback and a constant non singular input transformation these conditions are expressed in a very simple way in terms of integers which are feedback invariants for the system under consideration these feedback invariants are related either to the system infinite structure or to the reachability indices of the feedback reduced system

generalized linear systems with lumped or distributed parameters and differential vector spaces abstract by employing differential vector spaces we obtain results for linear systems with constant or varying coefficients and with lumped or distributed parameters which were only known for constant linear systems described by rational transfer matrices questions such as the characterization of input and output input output equivalence invertibility feedback decoupling and realization are investigated

fault isolation filter design for linear time invariant systems this paper is concerned with the problem of detecting and isolating multiple faults by a full order observer of the plant state we first obtain the fault isolability condition from the dual concept namely static state feedback decoupling a new full state observer design method is then developed to isolate simultaneous multiple faults the method can isolate m simultaneous faults with m output measurements such that the isolability condition is satisfied under zero initial error of state estimation asymptotic fault isolation results can also be obtained using the same observer design if the number of invariant eigenvalues is n m and if they are stable where n represents the system order m is the number of faults in the system in both cases m can be up to the system order n

transfer function matrix approach to decoupling problem with stability a simple necessary and sufficient condition for solvability of decoupling with internal stability for unity output feedback for non singular plants is proposed

block decoupling and arbitrary pole assignment for a linear right invertible system by dynamic compensation abstract the block decoupling of a linear right invertible system by dynamic compensation is studied the system structure of the block decoupled system is clarified from the viewpoint of the closed loop poles a dynamic compensator that realizes block decoupling and arbitrary pole assignment is proposed two examples are given to illustrate the design procedure of the dynamic compensator and its effectiveness

sensitivity reduction by strongly stabilizing controllers for mimo distributed parameter systems this note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time invariant multi input multioutput distributed parameter system the plant we consider has finitely many unstable zeros which are simple and blocking but can possess infinitely many unstable poles we obtain a necessary condition and a sufficient condition for the solvability of the problem using the matrix nevanlinna pick interpolation with boundary conditions we also develop a necessary and sufficient condition for the solvability of the interpolation problem and show an algorithm to obtain the solutions our method to solve the interpolation problem is based on the schur nevanlinna algorithm

strong stabilization of a class of mimo systems stabilization of finite dimensional linear time invariant multi input multi output plants by stable feedback controllers known as the strong stabilization problem is considered for a class of plants with restrictions on the zeros in the right half complex plane the plant class under consideration has no restrictions on the poles or on the zeros in the open left half complex plane or on the zeros at the origin or at infinity but only one finite positive real zero is allowed a systematic strongly stabilizing controller design procedure is proposed the freedom available in the design parameters may be used for additional performance objectives although the only goal here is strong stabilization in the special case of single input single output plants within the class considered the proposed stable controllers have order one less than the order of the plant

sensitivity minimization by strongly stabilizing controllers for a class of unstable time delay systems weighted sensitivity minimization is studied within the framework of strongly stabilizing stable hinfin controller design for a class of infinite dimensional systems this problem has been solved by ganesh and pearson for finite dimensional plants using nevanlinna pick interpolation we extend their technique to a class of unstable time delay systems moreover we illustrate suboptimal solutions and their robust implementation

optimal discriminating designs for several competing regression models the problem of constructing optimal designs for a class of regression models is considered we investigate a version of the tp optimality criterion as introduced by atkinson and fedorov 1975b and demonstrate that optimal designs with respect to this type of criteria can be obtained by solving nonlinear vector valued approximation problems we provide a characterization of the best approximations in this context and use these results to develop an efficient algorithm for the determination of the optimal discriminating designs the results are illustrated by fnumerical examples

synthesis of simultaneous stabilizing h controller controller in the chain scattering framework it has been shown in lee and soh 2004 that the problem of simultaneous stabilization of a finite collection of l linear time invariant plants such that each closed loop transfer function has an norm less than a prescribed performance level is equivalent to a simultaneous strongly stabilizing problem i e finding a single stable and norm bounded controller for associated l 1 unimodular plants such that each resulting closed loop system is stable and norm bounded this paper attempts to provide a solution to the simultaneous strongly stabilization problem a new sufficient condition in the form of the solution to only one algebraic riccati equation is provided for the existence of a strongly stabilizing controller for a given stable system obtained from the parameterization of stabilizing controllers with the parameterization of strongly stabilizing controllers provided in this paper a solution is given for the simultaneous strongly stabilization problem and hence

on the synthesis of stable spl hscr sup spl infin controllers a sufficient condition is derived for the existence of a stable suboptimal spl hscr sup spl infin controller it is shown that if a certain algebraic riccati equation determined from a parameterization of all suboptimal spl hscr sup spl infin controllers has a positive definite stabilizing solution then a stable spl hscr sup spl infin controller of order 2n can be constructed where n is the order of the generalized plant

block decoupling and pole assignment of singular systems a frequency domain approach the problem of block decoupling of singular systems via state feedback and regular input transformation is solved by following an approach based on the matrix fraction description mfd of the system the solvability condition is obtained from the numerator matrix of a coprime and column reduced mfd of the given system the characterization of the fixed poles is given and it is shown that all the non fixed poles can be arbitrarily assigned

h sup spl infin optimal and suboptimal controllers for infinite dimensional siso plants this paper presents a simple formula for h sup spl infin optimal and suboptimal controllers for unstable siso distributed plants with rational weighting functions the controller is expressed in terms of i inner and outer parts of the plant ii a finite dimensional spectral factor obtained from the weighting functions and iii a rational function satisfying certain interpolation conditions under certain genericity assumptions this rational function is of dimension less than or equal to n sub 1 l 1 n sub 1 l in the suboptimal case where l is the number of unstable poles of the plant and n sub 1 is the order of the sensitivity weighting function there are 2 n sub 1 l 2 n sub 1 l 1 in the suboptimal case linear equations which determine this rational function these linear equations can be written directly from the structure of the controller

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

brief on the strong stabilization and stable h controller design problems for mimo systems a state space based design method is developed to construct strongly stabilizing controllers for a class of mimo plants the problem is reduced to solving an algebraic riccati equation are which appears in the solution of a two block h problem strongly stabilizing controllers designed here are of the same order as the plant two sets of finite dimensional strongly stabilizing controllers are parameterized in terms of linear fractional transformations further optimization guidelines are given to find stable h controllers from these parameterizations stability robustness margins with respect to coprime factor uncertainties are determined for the controllers designed from the proposed method

a precompensator design to achieve the decoupling condition in the frequency domain this paper deals with the problem of designing a precompensator by using the frequency domain approach for linear systems having weak inherent coupling such that the composite system will be decouplable through linear state variable feedback l s v f alone three algorithms are presented for such a purpose the first one makes use of a new theorem for dynamic decoupling through l s v f alone while the other two make use of the interactor concept the algorithms always yield stable precompensators moreover the controllability and observability of the composite system are guaranteed

new results about morgan s problem some aspects of the nonsquare morgan s problem are considered in particular it is shown that the condition given by j descusse et al 1986 to solve this problem is not sufficient it is also shown that the essential orders are not necessarily preserved in the static decoupling problem a necessary and sufficient condition for static decoupling of a system without modifying the essential orders is given for the case k p 1 where p is the number of outputs and k is the rank at infinity of the proper part of the interactor

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

stable controller synthesis for linear time invariant systems this paper is concerned with the problem of suboptimal stable mixed h 2 h x control for linear time invariant systems the designed controller with the same order as that of the considered system is required to satisfy a prescribed h x performance bound or a prescribed degree of stability by reducing the stable controller synthesis problem to a multiobjective state feedback control problem for two different state models sufficient conditions for the solvability of the considered problem are given in terms of solutions to algebraic riccati equations and matrix inequalities an lmi based iterative algorithm is developed to solve the stable controller synthesis problem the proposed algorithm is shown to be convergent examples are given to illustrate the proposed methods

robust h control of a nonlinear uncertain system via a stable nonlinear output feedback controller a new approach to solving a nonlinear robust h control problem using a stable nonlinear output feedback controller is presented in this article the class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global lipschitz conditions describing the admissible uncertainties and nonlinearities respectively the nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller the h control objective is to obtain an absolutely stable closed loop system with a specified disturbance attenuation level the solution to this control problem involves stabilising solutions to parametrised algebraic riccati equations we apply a differential evolution algorithm to solve a non convex nonlinear optimisation problem arising in the controller synthesis

static state feedback triangular block decoupling for arbitrary systems a state space method abstractin this paper the static state feedback triangular block decoupling problem for a general system described by a b c d quadruples is studied necessary and sufficient conditions which are numerically verifiable are obtained and a numerically reliable decoupling method is established in the state space two examples are solved by our method which show the effectiveness

diagonal decoupling of linear systems by static state feedback a solution is presented to the long standing open problem of linear systems theory diagonal decoupling by static state feedback the earliest known investigation of system decoupling dates back to 1934 a state space formulation of the problem appeared in 1964 and a solution for square and invertible systems followed in 1967 the case of right invertible systems however has withstood all past efforts to obtain a solution save for several special cases the present formulation avoids restrictive hypotheses concerning system and decoupling feedback the existence of a solution is shown to depend on the existence of three lists of integers conditioned solely by system invariants with respect to the permissible transformations

an algorithm for interpolation with units in h with applications to feedback stabilization abstract the problem of finding a unit in h i e an h function the inverse of which is also h which interpolates to given points in the right half plane has important applications in a number of feedback stabilization problems i e strong stabilization and simultaneous stabilization an algorithm for computing such interpolating units is presented which requires a lower degree unit than other available algorithms

h sub spl infin strong stabilization this note presents a technique for designing stable h sub spl infin controllers similar to some methods in the existing literature the proposed method also uses the parameterization of all suboptimal h sub spl infin controllers so that the stable h sub spl infin design problem can be conservatively converted into another 2 block standard h sub spl infin problem however a weighting function is introduced in this method to alleviate the conservativeness of the previous formulations it is further shown that the resulting high order controller can be significantly reduced by a two step reduction algorithm numerical examples are presented to demonstrate the effectiveness of the proposed method

synthesis of stable h controller via the chain scattering framework abstract a sufficient condition for the existence of suboptimal stable stabilizing h controllers is given by exploiting the free parameter in the parameterization of stabilizing controllers and using the chain scattering framework we reformulate the h strong stabilization problem as an equivalent h optimization problem which can be solved via only one algebraic riccati equation a parameterization of all suboptimal stable stabilizing h controllers is also given

robust h infty control of an uncertain system via a stable output feedback controller this technical note presents a new approach to the robust control of an uncertain system via a stable output feedback controller the uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints the controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation the main result involves solving a state feedback version of the problem by solving an algebraic riccati equation dependent on a set of scaling parameters then two further algebraic riccati equations are solved which depend on a further set of scaling parameters

an efficient design for model discrimination and parameter estimation in linear models summary we consider experimental designs in a regression set up where the unknown regression function belongs to a known family of nested linear models the objective of our design is to select the correct model from the family of nested models as well as to estimate efficiently the parameters associated with that model we show that our proposed design is able to choose the true model with probability tending to one as the number of trials grows to infinity we also establish that our selected design converges to the optimal design distribution for the true linear model ensuring asymptotic efficiency of least squares estimators of model parameters

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

brief canonical h state space parametrization in this paper a new parametrization of all stable multivariable systems satisfying a given bound on their h norm is presented this parametrization extends previous results in the sense that it uses a minimum amount of parameters and that it comprises also proper systems the parametrization has a number of parameters similar to that of classical multivariable state space forms the construction of the parametrization is based on the bounded real lemma and the reduction to hessenberg form by unitary similarity transformations the parametrization can be used to select the free parameters in a class of all h controllers in order to include regulation constraints

unit interpolation in h bounds of norm and degree of interpolants abstract this paper studies the problem of unit interpolation in h specifically bounds of the norm and degree of interpolants are obtained using the nevanlinna pick interpolation theory also simpler bounds are given using the poincare metric these results indicate that strong stabilization and simultaneous stabilization need a cautious approach if the system is ill conditioned in fact it is demonstrated that the degree of stable compensator is not bounded for the class of plants with fixed degree also an example shows that there is a class of plants for which the sensitivity can be made small only if unstable compensators are used

block decoupling of generalized state space systems abstract the problem of input output block decoupling of generalized state space systems via a regular static state feedback law is studied for the first time the necessary and sufficient conditions for the problem to have a solution are established the necessary and sufficient conditions for block decoupling with simultaneous stabilizability and the necessary and sufficient conditions for block decoupling with simultaneous arbitrary assignment of the system poles are established 1997 elsevier science ltd

robust optimal extrapolation designs summary we study robustness properties of optimal extrapolation designs at a single point under various model assumptions a curious result is the efficiency of the optimal extrapolation design for a polynomial of degree m is the same whether the true underlying model is a polynomial of degree k or m k k 1 2 m 1 in addition the loss in efficiency of the optimal extrapolation designs is between 40 50 when we overestimate the degree of the polynomial model and the extrapolated point is far from the design space we propose a new class of optimality criteria for extrapolation the new optimal extrapolation designs are shown to be more efficient and robust to the regression functions they enjoy good power for discriminating among polynomial models and if the extrapolated point is sufficiently far from the design space they coincide with the optimal discrimination designs studied in dette 1994

robust t optimal discriminating designs this paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the t optimality criterion introduced by atkinson and fedorov 1975a t optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification as a solution of this problem we propose a bayesian and standardized maximin approach to construct robust and efficient discriminating designs on the basis of the t optimality criterion it is shown that the corresponding bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria for the problem of discriminating between two polynomial regression models which differ in the degree by two the robust t optimal discriminating designs can be found explicitly the results are illustrated in several examples ams subject classification 62k05

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process