linear approximation of transfer function with a pole of fractional power two methods for the linear approximation of a transfer function with a pole of fractional power are presented analog circuit models are developed and their frequency response curves and step response curves are compared it was found that the pade method gives a better approximation than wang and hsia s method within the frequency limit as specified

fractional calculus for interval valued functions abstract we use a generalization of the hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval valued functions the properties of riemann liouville fractional integral riemann liouville fractional derivative and caputo fractional derivative for interval valued functions are investigated several examples are presented to illustrate the concepts and results

robust stabilization for rectangular descriptor fractional order interval systems with order 0 α 1 abstract this paper considers the normalization and stabilization of rectangular descriptor fractional order interval systems with fractional order 0

regular fractional factorial designs with minimum aberration and maximum estimation capacity using the approach of finite projective geometry we make a systematic study of estimation capacity a criterion of model robustness under the absence of interactions involving three or more factors some general results providing designs with maximum estimation capacity are obtained in particular for two level factorials it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible we also explore the connection with minimum aberration designs under which the sizes of the alias sets of two factor interactions which are not aliased with main effects are the most uniform possible

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 paper pseudo state feedback stabilization of commensurate fractional order systems this paper addresses the problem of pseudo state feedback stabilization of commensurate fractional order systems fos in the proposed approach linear matrix inequalities lmi formalism is used to check if the pseudo state matrix eigenvalues belong to the fos stability region of the complex plane a review of lmi stability conditions is first proposed for fractional order 0 n 1 and 1 n 2 the paper then focuses particularly on the case 0 n 1 as the stability region is non convex and associated lmi condition is not as straightforward to obtain as in the case 1 n 2 a new lmi stability condition is thus proposed based on this condition a necessary and sufficient lmi method for the design of stabilizing controllers is given this method paves the way for extension to fos of various lmi based results among these possible extensions a first result on robust control of polytopic fractional order systems is given in this paper

robust stability and stabilization of fractional order interval systems with the fractional order alpha the 0 alpha 1 case this technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional order interval systems with the fractional order satisfying 0 1 and then a sufficient condition for the robust asymptotical stabilization of such fractional order interval systems is derived all the results are obtained in terms of linear matrix inequalities finally two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional order interval systems

robust stability analysis of fractional order uncertain singular nonlinear system with external disturbance this paper investigates robust stability for fractional order fo singular nonlinear systems the fo system is disturbed by external uncertainty and disturbance a central analysis technique is enabled by proposing a fundamental boundedness lemma for the first time this lemma is used for robust stability analysis of fo systems especially for mittag leffler stability analysis of fo nonlinear systems more importantly how to obtain a more accurate bound is given to reduce conservative an fo proportional derivative pd controller is proposed to normalize the fo singular system furthermore a criterion for stability of the normalized fo nonlinear systems is provided by linear matrix inequalities lmis finally two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

controller design with regional pole constraints a design procedure is developed that combines linear quadratic optimal control with regional pole placement specifically a static and dynamic output feedback control problem is addressed in which the poles of the closed loop system are constrained to lie in specified regions of the complex plane these regional pole constraints are embedded within the optimization process by replacing the covariance lyapunov equation by a modified lyapunov equation whose solution in certain cases leads to an upper bound on the quadratic cost functional the results include necessary and sufficient conditions for characterizing static output feedback controllers with bounded performance and regional pole constraints sufficient conditions are also presented for the fixed order i e full and reduced order dynamic output feedback problem with regional pole constraints circular elliptical vertical strip parabolic and section regions are considered

a neural network for linear matrix inequality problems gradient type hopfield networks have been widely used in optimization problems solving the paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities lmis which are commonly encountered in the robust control system analysis and design the solution process is parallel and distributed in neural computation the proposed networks are proven to be stable in the large representative lmis such as generalized lyapunov matrix inequalities simultaneous lyapunov matrix inequalities and algebraic riccati matrix inequalities are considered several examples are provided to demonstrate the proposed results to verify the proposed control scheme in real time applications a high speed digital signal processor is used to emulate the neural net based control scheme

linear quadratic control with stability degree constraint abstract the problem of static state feedback linear quadratic lq optimal control subject to a prescribed degree of stability for the closed loop system is considered in this paper a necessary optimality condition is given via the lagrange multiplier method a globally convergent algorithm is provided to solve the optimization problem it is shown that the algorithm recovers the standard lq feedback gain provided the desired stability degree is small enough to be within the range by the standard lq design as for other cases the optimum occurs on the boundary of the region a numerical example shows that the proposed algorithm provides a better design compared to the existing methods

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

robust normalization and stabilization of uncertain descriptor systems with norm bounded perturbations this note is concerned with the problem of the so called quadratic normalization and stabilization via both proportional and derivative state feedback pdsf and proportional and derivative output feedback pdof for uncertain descriptor systems with norm bounded perturbations necessary and sufficient conditions are presented in terms of linear matrix inequalities lmis or quadratic matrix inequalities qmis by using a simple idea of changing the problem to the corresponding stabilization problem of an augmented uncertain system

optimal blocking of two level factorial designs summary blocking of two level factorial designs is considered for block sizes 2 and 4 using the method of fractional partial confounding a d and e optimal designs are obtained for block size 2 within the class of orthogonal designs for which main effects and two factor interactions are all orthogonal to each other before allowing for blocking a d and e optimal designs are obtained for block size 4 within the class of orthogonal designs with main effects orthogonal to blocks the designs obtained also have other favourable properties including orthogonal estimation of effects and orthogonality to superblocks

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

robust stabilization of uncertain descriptor fractional order systems this paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional order systems with the fractional order a satisfying 0 a 2 the results are obtained in terms of linear matrix inequalities the parameter uncertainties are assumed to be time invariant and norm bounded appearing in the state matrix a necessary and sufficient condition for the normalization of uncertain descriptor fractional order systems is given via linear matrix inequality lmi formulation the state feedback control to robustly stabilize such uncertain descriptor fractional order systems with the fractional order a belonging to 0 a 2 is derived two numerical examples are given to demonstrate the applicability of the proposed approach

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

optimal blocking schemes for 2n and 2n p designs systematic sources of variations in factorial experiments can be effectively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks for full factorial designs optimal blocking schemes are obtained by applying the minimum aberration criterion to the block defining contrast subgroup a related concept of order of estimability is proposed for fractional factorial designs because of the intrinsic difference between treatment factors and block variables the minimum aberration approach has to be modified a concept of admissible blocking schemes is proposed for selecting block designs based on multiple criteria the resulting 2 n and 2 n p designs are shown to have better overall properties for practical experiments than those in the literature

interval stability and stabilization of linear stochastic systems this technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time invariant systems first the notion of beta alpha stability of stochastic systems is defined and some relationships among the beta alpha stability the decay rate of system state response and the second order moment lyapunov exponent are revealed we then address the beta alpha stabilization problem and give a sufficient condition via a linear matrix inequality approach

2n l designs with weak minimum aberration since not all 2 n l fractional factorial designs with maximum resolution are equally good fries and hunter introduced the minimum aberration criterion for selecting good 2 n l fractional factorial designs with the same resolution we modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept using some techniques from finite geometry we construct 2 n l fractional factorial designs of resolution iii with weak minimum aberration further several families of 2 n l fractional factorial designs of resolution iii and iv with minimum aberration are obtained

blocking in regular fractional factorials a projective geometric approach a projective geometric characterization is given of the existence of any regular main effect s n k design in s blocks it leads to a constructive method for finding a maximal blocking scheme for any given fractional factorial design a useful sufficient condition for admissible block designs is given in terms of the minimum aberration property of a certain unblocked design

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

lmi stability conditions for fractional order systems after an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives also denoted fractional order systems this paper deals with linear matrix inequality lmi stability conditions for fractional order systems under commensurate order hypothesis it is shown that a direct extension of the second lyapunov s method is a tedious task if the fractional order n is such that 0 n 1 the stability domain is not a convex region of the complex plane however through a direct stability domain characterization three lmi stability analysis conditions are proposed the first one is based on the stability domain deformation and the second one on a characterization of the instability domain which is convex the third one is based on generalized lmi framework these conditions are applied to the gain margin computation of a crone suspension

lmi based reset mathcal h _ infty design for linear continuous time plants in this technical note an optimization based synthesis of a multi objective reset controller for linear plants is presented the result allows designing via convex tools with a line search a multi objective reset controller optimizing both the exponential converging rate and the mathcal l 2 gain a novel peculiarity of our scheme is that the underlying linear flow dynamics is not necessarily stabilizing this last property is the consequence of taking into account where the flowing trajectories lay and lead to improved performance especially in terms of decay rate some simulations illustrate the usefulness of our techniques

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

technical communique robust stabilization for uncertain discrete singular systems this paper considers the problem of robust stabilization for uncertain discrete singular systems subject to time invariant norm bounded unstructured uncertainty in the state matrix the problem we address is the design of state feedback controllers such that the resulting closed loop system is regular causal as well as stable for all admissible uncertainties in this connection the concept of generalized quadratic stabilizability is defined in terms of matrix inequalities a necessary and sufficient condition for generalized quadratic stabilizability is derived under certain assumptions when this condition holds the explicit formula of a state feedback controller solving the problem is also given the results can be viewed as extensions of existing results on robust stabilization of uncertain discrete standard state space systems

blocked regular fractional factorial designs with maximum estimation capacity in this paper the problem of constructing optimal blocked regular fractional factorial designs is considered the concept of minimum aberration due to fries and hunter is a well accepted criterion for selecting good unblocked fractional factorial designs cheng steinberg and sun showed that a minimum aberration design of resolution three or higher maximizes the number of two factor interactions which are not aliases of main effects and also tends to distribute these interactions over the alias sets very uniformly we extend this to construct block designs in which i no main effect is aliased with any other main effect not confounded with blocks ii the number of two factor interactions that are neither aliased with main effects nor confounded with blocks is as large as possible and iii these interactions are distributed over the alias sets as uniformly as possible such designs perform well under the criterion of maximum estimation capacity a criterion of model robustness which has a direct statistical meaning some general results on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach

inhomogeneous markov approach to percolation theory based propagation in random media in recent years it has been shown that ray propagation in two dimensional 2d uniform random percolation lattices is well approximated by stochastic processes two of the probabilistic interpretations can be solved exactly but impose some additional restrictions on the ray dynamics the 1999 model by g franceschetti demands that ray reflections inside the lattice are independent and identically distributed iid and the 2006 model by a martini assumes that for the analysis of vertical ray penetration reflections on vertical lattice cell faces can be neglected in this paper we present a 2d generalization of the 1999 model that does not rely on the iid assumption it is based on a set of coupled iteration formulas for right stochastic matrices that describe a time inhomogeneous markov process upon expanding the space of transition states the iterative process can be recast in the projection of a time homogeneous markov chain thus the perron frobenius theorem can be applied to analyze the stationary states of the process which leads to a simple analytical expression for the probability of a ray ensemble reaching a specified lattice level after infinitely many reflections we discuss different boundary conditions at the absorbing barriers of the ray propagation process and show that 1 by imposing the iid assumption the 1999 model by g francescetti can be recovered and 2 a one dimensional reduction of the approach exactly leads to the 2006 model by a martini the presented stochastic approach provides a framework in which basic assumptions of probabilistic interpretations of percolation theory based ray propagation can be studied in some detail it also allows for the consistent derivation of the stationary probability states which are needed to apply the approach to a wider range of phenomena such as internal source ray propagation in both uniform and nonuniform random media

sliding mode design via quadratic performance optimization with pole clustering constraint we consider a novel method for designing the sliding mode that minimizes the quadratic performance while keeping a pole clustering constraint our approach is based on the manipulations of linear matrix inequalities lmis imposed by the design objectives for this purpose we newly propose lmi conditions for the quadratic performance optimization and the pole clustering problem respectively in a full order state then they are combined in the lmi framework that is typically devised for the sliding mode design in the convex form an effort is made to reduce the generic conservatism by allowing different lyapunov matrices in addition a class of polytope uncertain systems is addressed to illustrate the advantages of the proposed method

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

blocked regular fractional factorial designs with minimum aberration this paper considers the construction of minimum aberration ma blocked factorial designs based on coding theory the concept of minimum moment aberration due to xu 2003 for unblocked designs is extended to blocked designs the coding theory approach studies designs in a row wise fashion and therefore links blocked designs with nonregular and supersaturated designs a lower bound on blocked wordlength pattern is established it is shown that a blocked design has ma if it originates from an unblocked ma design and achieves the lower bound it is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros sufficient conditions are given for constructing ma blocked designs from unblocked ma designs the theory is then applied to construct ma blocked designs for all 32 runs 64 runs up to 32 factors and all 81 runs with respect to four combined wordlength patterns

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

selecting defining contrasts and confounded effects in p n m factorial experiment fractional factorial designs presented in standard tables are not always suitable when some factors are more likely than others to interact if the fraction is small compared to the total number of treatments the selection of defining contrasts to generate a design meeting specified requirements is not straightforward a systematic procedure is given for selecting defining contrasts and confounded effects in p n m factorial designs where p 2 is prime

ray propagation in a random lattice a maximum entropy anomalous diffusion process the typical model for diffusion in disordered systems is that of a random walk that proceeds in discrete steps over a random lattice where not all the nearest sites can be reached at each step we study the related problem of ray propagation in percolating lattices and observe that it follows an anomalous diffusion process whose appropriate metric is the manhattan distance defined by the lattice geometry the proposed solution is the one that exhibits the maximum shannon s entropy among all propagation processes with appropriate moment constraints imposed by the geometry of the lattice ray propagation in percolating lattices has been recently proposed as a model for urban area propagation of radio waves we discuss implications of our results in this scenario

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

pole assignment in a specified disk the problem of assigning all poles of a closed loop system in a specified disk by state feedback is considered for both continuous and discrete systems a state feedback control law is determined by using a discrete riccati equation this kind of pole assignment problem is named d pole assignment and its relation to the optimal control problem and its robustness properties are discussed the gain and phase margins for all closed loop poles to stay inside the specified disk d are determined for the proposed control

characterization of minimum aberration 2 sp n k designs in terms of their complementary designs a general result is obtained that relates the word length pattern of a 2 n k design to that of its complementary design by applying this result and using group isomorphism we are able to characterize minimum aberration 2 n k designs in terms of properties of their complementary designs the approach is quite powerful for small values of 2 n k n 1 in particular we obtain minimum aberration 2 n k designs with 2 n k n 1 1 to 11 for any n and k

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

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

theory of optimal blocking of 2 n m designs in this paper we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment defining words and block defining words the concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design by blending techniques of coding theory and finite projective geometry we obtain combinatorial identities that govern the relationship between the blocking wordlength pattern of a blocked 2 n m design and the split wordlength pattern of its blocked residual design based on these identities we establish general rules for identifying minimum aberration blocked 2 n m designs in terms of their blocked residual designs using these rules we study the structures of some blocked 2 n m designs with minimum aberration

markov approach to percolation theory based propagation in random media for line of sight links in random media or urban areas propagation may be approximated through sequential reflections of an optical ray in a two dimensional medium of disordered lossless scatterers franceschetti approximated such percolation based optical ray propagation by a markov process with two absorbing barriers provided numerical solutions for the probability of a ray passing through the percolation lattice and solved both approximately and exactly a corresponding problem based on the theory of martingales in this paper we solve exactly the markov theoretical formulation of the problem and prove that both the markov and martingale approaches are equivalent our proof is an application of the perron frobenius theory which provides an elegant framework for the study of the asymptotic behavior of stochastic processes we demonstrate that for a wide range of vacancies and incident angles the exact solution of the markov theoretical formulation performs significantly better than the commonly used wald approximation in the martingale approach this has a number of implications on the accuracy of the model especially for low density propagation media

fundamental connections among the stability conditions using higher order time derivatives of lyapunov functions for the case of linear time invariant systems abstract it has already been recognized that looking for a positive definite lyapunov function such that a high order linear differential inequality with respect to the lyapunov function holds along the trajectories of a nonlinear system can be utilized to assess asymptotic stability when the standard lyapunov approach examining only the first derivative fails in this context the main purpose of this paper is on one hand to theoretically unveil deeper connections among existing stability conditions especially for linear time invariant lti systems and from the other hand to examine the effect of the higher order time derivatives approach on the stability results for uncertain polytopic lti systems in terms of conservativeness to this end new linear matrix inequality lmi stability conditions are derived by generalizing the concept mentioned above and through the development relations among some existing stability conditions are revealed examples illustrate the improvement over the quadratic approach

propagation without wave equation toward an urban area model propagation in random media is a topic of great interest whose application fields include among others the so called last mile problem as well as the modeling of dense urban area radio communication channels a simple scenario for this issue is considered with an optical ray propagation across a medium of disordered lossless scatterers the propagation medium behaves like a percolating lattice and the goal is to characterize statistically the propagation depth in the medium as a function of the density g of scatterers and of spl theta the ray incidence angle to the best of our knowledge this approach is totally new the problem is mathematically formulated as a random walk and the solutions are based on the theory of the martingale random processes the obtained approximate analytical formulas have been validated by means of numerical simulations demonstrating the applicability of the proposed model for a wide range of the global parameters q and spl theta we believe that our results may constitute a promising first step toward the solution of more complicated propagation models and a wide class of communication problems

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

some identities on q sp n m designs with application to minimum aberration designs chen and hedayat and tang and wu studied and characterized minimum aberration 2 n m designs in terms of their complemetary designs based on a new and more powerful approach we extend the study to identify minimum aberration q n m designs through their complementary designs by using macwilliams identities and krawtchouk polynomials in coding theory we obtain some general and explicit relationships between the wordlength pattern of a q n m design and that of its complementary design these identities provide a powerful tool for characterizing minimum aberration q n m designs the case of q 3 is studied in more details

on fractional calculus and fractional multipoles in electromagnetism using the concept and tools of fractional calculus we introduce a definition for fractional order multipoles of electric charge densities and we show that as far as their scalar potential distributions are concerned such fractional order multipoles effectively behave as intermediate sources bridging the gap between the cases of integer order point multipoles such as point monopoles point dipoles point quadrupoles etc this technique which involves fractional differentiation or integration of the dirac delta function provides a tool for formulating an electric source distribution whose potential functions can be obtained by using fractional differentiation or integration of potentials of integer order point multipoles of lower or higher orders as illustrative examples the cases of three dimensional point source and two dimensional line source problems in electrostatics are treated in detail and an extension to the time harmonic case is also addressed in the three dimensional electrostatic example we suggest an electric charge distribution which can be regarded as an intermediate case between cases of the electric point monopole point charge and the electric point dipole point dipole and we present its electrostatic potential which behaves as r sup 1 spl alpha p sub spl alpha cos spl theta where 0 spl alpha 1 and p sub spl alpha spl middot is the legendre function of noninteger degree spl alpha thus denoting this charge distribution as a fractional 2 sup spl alpha pole at the two limiting cases of spl alpha 0 and spl alpha 1 this fractional 2 sup spl alpha pole becomes the standard point monopole and point dipole respectively a corresponding intermediate fractional order multipole is also given for the two dimensional electrostatic case potential applications of this treatment to the image method in electrostatic problems are briefly mentioned physical insights and interpretation for such fractional order 2 sup spl alpha poles are also given

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

robust h control for linear time invariant systems with norm bounded uncertainty in the input matrix abstract this paper focuses on the problem of robust h control design for a class of linear time invariant systems with uncertainty in the state space model we consider uncertain systems with norm bounded parameter uncertainty in the input matrix the paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an h norm bound constraint on disturbance attenuation paralleling to the theory of robust control the robust h control problem is solved via the notion of quadratic stabilization with an h norm bound constraint necessary and sufficient conditions for quadratic stabilization with an h norm bound are derived it is shown that the solution to this problem involves solving a parameter dependent algebraic riccati equation the results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and h optimal control

a random walk model of wave propagation this paper shows that a reasonably accurate description of propagation loss in small urban cells can be obtained with a simple stochastic model based on the theory of random walks that accounts for only two parameters the amount of clutter and the amount of absorption in the environment despite the simplifications of the model the derived analytical solution correctly describes the smooth transition of power attenuation from an inverse square law with the distance to the transmitter to an exponential attenuation as this distance is increased as it is observed in practice our analysis suggests using a simple exponential path loss formula as an alternative to the empirical formulas that are often used for prediction results are validated by comparison with experimental data collected in a small urban cell

fractional resolution and minimum aberration in blocked 2 n k designs systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks this is accomplished through the use of blocking factors the concepts of resolution and minimum aberration design optimization criteria ordinarily used to rank unblocked fractional factorial designs are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup some limited theoretical results are derived and tables of minimumaberration blocked two level fractional factorial designs are presented and considered the relationship between clear effects effects that are estimable when higher order effects are assumed negligible and minimum aberration in the presence of blocking is discussed

fractional factorial designs with admissible sets of clear two factor interactions we consider the problem of selecting two level fractional factorial designs that allow joint estimation of all main effects and some specified two factor interactions 2fi s without aliasing from other 2fi s this problem is to find among all 2 m p designs with given m and p those resolution iv designs whose sets of clear 2fi s contain the specified 2fi s as subsets we use a linear graph to represent the set of clear 2fi s for a resolution iv design where each line connecting two vertexes represents a clear 2fi between the factors represented by the two vertexes we call a 2 m p resolution iv design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2 m p resolution iv design we show that all even resolution iv designs are inadmissible we then use a classical subgraph isomorphism algorithm to determine all admissible designs of 32 64 and 128 runs this leads to a concise catalog of all admissible designs of 32 and 64 runs and a lengthy but substantially re