pole assignment by output feedback using cylindrical algebraic decomposition recently a new polynomial method for pole assignment by static output feedback has been developed in this paper we show how this method can be generalized to partial pole clustering some poles are exactly assigned the others being clustered in a specified region of the complex plane a constructive and systematic algorithm for the numerical resolution of both problems the collins cylindrical algebraic decomposition algorithm is presented and applied to an illustrative example

on the distance spectrum of distance regular graphs abstract the distance matrix of a simple graph g is d g d i j where d i j is the distance between ith and jth vertices of g the spectrum of the distance matrix is known as the distance spectrum or d spectrum of g a simple connected graph g is called distance regular if it is regular and if for any two vertices x y g at distance i there are constant number of neighbors c i and b i of y at distance i 1 and i 1 from x respectively in this paper we prove that distance regular graphs with diameter d have at most d 1 distinct d eigenvalues we find an equitable partition and the corresponding quotient matrix of the distance regular graph which gives the distinct d eigenvalues we also prove that distance regular graphs satisfying b i c d 1 have at most d 2 2 distinct d eigenvalues applying these results we find the distance spectrum of some distance regular graphs including the well known johnson graphs finally we also answer the questions asked by lin et al 16

the distance signatures of the incidence graphs of affine resolvable designs abstract in this note we determined the distance signatures of the incidence matrices of affine resolvable designs this proves a conjecture by kohei yamada

robust pole assignment in singular control systems abstract necessary conditions are given for the problem of pole assignment by state feedback in singular linear systems descriptor systems to have a solution which is regular and nondefective for a robust solution such that the assigned closed loop poles are insensitive to perturbations in the system data the same conditions must hold it can be shown that these conditions are also sufficient for the existence of a feedback which assigns the maximum possible number of finite poles with regularity these results provide the basis of a procedure for constructing closed loop semistate systems with given poles guaranteed regularity and maximum robustness

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

robust control for linear systems with structured state space uncertainty abstract a recent sufficient condition for the stability robustness of linear systems with time varying norm bounded state space uncertainty is extended to include the structure of the uncertainty our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix therefore this robustness result is especially well suited to the design of control systems using eigenstructure assignment when the uncertainty is time invariant our norm is also an upper bound on the incremental eigenvalue perturbations we also consider the use of perron weightings to reduce conservatism and the extension of the results to discrete time systems

a closed form solution to the discrete time kalman filter and its applications abstract this paper presents a closed form solution to the discrete time kalman filter and its applications we first represent the kalman filter in terms of model parameters without using the riccati equation and requiring any artificial conditions such as invertibility of a system matrix and no system noises replacing the initial time with the fixed lag time to achieve the finite memory with respect to inputs and outputs and choosing the proper initial covariances on the recent finite horizon we easily obtain the minimum variance finite memory filter and then propose its iterative computation algorithm as another application a closed form solution to the difference riccati equation on the finite horizon is utilized to obtain a stabilizing gain matrix of a luenberger type filter as in ackermann s formula

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

reliability based code search algorithms for maximum likelihood decoding of block codes efficient code search maximum likelihood decoding algorithms based on reliability information are presented for binary linear block codes the codewords examined are obtained via encoding the information set utilized for encoding comprises the positions of those columns of a generator matrix g of the code which for a given received sequence constitute the most reliable basis for the column space of g substantially reduced computational complexity of decoding is achieved by exploiting the ordering of the positions within this information set the search procedures do not require memory the codeword to be examined is constructed from the previously examined codeword according to a fixed rule consequently the search algorithms are applicable to codes of relatively large size they are also conveniently modifiable to achieve efficient nearly optimum decoding of particularly large codes

eigenvalue assignment in a single input linear system a procedure for eigenvalue assignment in a single input linear system in hessenberg form is described the procedure uses real arithmetic throughout and includes a facility for estimating the robustness of the assigned eigenvalues the assigned eigenvalues may be real or complex simple or multiple

on distance matrices and laplacians we consider distance matrices of certain graphs and of points chosen in a rectangular grid formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved if d is the distance matrix of a tree then we obtain certain results for a perturbation of d 1 as an example it is shown that if l is the laplacian matrix of an arbitrary connected graph then d 1 l 1 is an entrywise positive matrix we consider the distance matrix of a subset of a rectangular grid of points in the plane if we choose m k 1 points not containing a closed path in an m k grid then a formula for the determinant of the distance matrix of such points is obtained

a robust optimal model matching control a deductive design approach is proposed to develop an optimal feedback control while preserving quantitative robustness and noise rejection properties the design procedure involves the minimization of a suitably selected performance index to reflect a required model matching following objective gradient projection schemes applied to the performance index and feasible constraints are used to accomplish the design tradeoff a mechanical manipulator control system example is employed as a vehicle to illustrate the overall design selection and optimization uncertainty of the system description is included as a feature of the example

advanced information of parity bits for decoding short linear block codes using the a algorithm the a algorithm for decoding linear block codes is known to be an efficient tree search method for decoding short linear block codes we propose to employ the early acquired information of some parity bits to speed up the tree search analysis for the number of required information bits for obtaining the parity bits is provided in addition two versions of the modified a algorithm which take advantage of the advanced information of parity bits are provided simulation results show that there is advantage in reducing the number of search tree edges in each proposed version as compared with two existing a algorithms which do not consider the early information of parity bits

computationally efficient soft decision decoding of linear block codes based on ordered statistics soft decision decoding of a linear block code using the most reliable basis corresponding to each received word is investigated based either on probabilistic properties or on the structure of the code considered three improvements to the algorithm devised by fossorier and lin see ibid vol 41 no 9 p 1379 1396 1995 are presented these modifications allow large computation savings or significant decoding speedup with little error performance degradation first a reduced probabilistic list of codeword candidates is associated with order i reprocessing of a given code it results in a large reduction of the maximum number of computations with a very small degradation in performance then a probabilistic stopping criterion is introduced for order 0 reprocessing this new test significantly decreases the average number of computations when appropriately implemented finally the application of the algorithm to coset decoding is considered for u u v constructed codes in addition to the conventional coset decoding a new adaptive practically optimum coset decoding method is presented where at each reprocessing stage the number of surviving cosets decreases suboptimum closest coset decoding is also investigated it is shown that two stage decoding with the algorithm of fossorier and lin offers a large variety of choices since the reprocessing order of each stage can be determined independently

stability robustness of almost linear state equations sufficient conditions for stability robustness of finite dimensional autonomous systems are discussed the system comprises a stable linear nominal part and different types of unstructured norm bounded perturbations quantitative sufficient conditions for stability robustness are introduced for the case in which the perturbations are almost linear in the sense that both the size and the derivative of the perturbations are bounded these conditions describe a tradeoff between the size of the perturbations and their distance from linearity the arbitrary nonlinear case and a special linear case are shown to be limiting cases of the almost linear type as an illustration the same quantitative sufficient conditions for stability are applied to a system with slowly varying linear perturbations

graphs whose distance matrix has at most three negative eigenvalues abstract let d g be the distance matrix of a connected simple graph g the negative inertia of d g denoted by n d g is the number of negative eigenvalues of d g in this paper we determine all connected graphs g whose distance matrix d g has at most three negative eigenvalues

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

connectivity diameter independence number and the distance spectral radius of graphs abstract the distance spectral radius of a graph is the largest eigenvalue of its distance matrix x l zhang 2012 31 determined the n vertex graphs of given diameter with the minimum distance spectral radius in this paper we generalize this result by characterizing the graphs of order n with given connectivity and diameter having minimum distance spectral radius in addition we determine the minimum distance spectral radius of graphs among the n vertex graphs with given connectivity and independence number and characterize the corresponding extremal graph thus determining the minimum distance spectral radius of graphs among n vertex graphs with given connectivity resp independence number

soft decision decoding of linear block codes using preprocessing and diversification order w reprocessing is a suboptimal soft decision decoding approach for binary linear block codes in which up to w bits are systematically flipped on the so called most reliable information basis mrb this correspondence first incorporates two preprocessing rules into order w reprocessing and shows that with appropriate choice of parameters the proposed order w reprocessing with preprocessing requires comparable complexity to order w reprocessing but achieves asymptotically the performance of order w 2 reprocessing to complement the mrb a second basis is employed for practical snrs and this approach is systematically extended to a multibasis order w reprocessing scheme for high signal to noise ratios snrs it is shown that the proposed multibasis scheme significantly enlarges the error correction radius a commonly used measure of performance at high snrs over the original single basis order w reprocessing as a by product this approach also precisely characterizes the asymptotic performance of the well known chase and generalized minimum distance gmd decoding algorithms the proposed algorithm successfully decodes the 192 96 reed solomon concatenated code and the 256 147 extended bch code in near optimal manner within 0 01 db at a block error rate of 10 5 with affordable computational cost

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

approximate pole assignment a novel approach and some new algorithms for the pole assignment problem of a controllable time invariant linear multivariable system with linear state or output feedback are presented the main theme of the approach and the algorithms is to satisfy some constraints in the problem approximately various rank 1 update algorithms can then be derived depending on different extents to which the constraints are approximated functionals have to be minimized when eigenvectors of the closed loop system are chosen a perturbation analysis on the effect of the approximation and several numerical examples will be presented

a new robust stability measure for state feedback systems abstract this brief paper proposes the use of sensitivities of each individual system pole to measure robust stability of state feedback systems compared with the existing measures of this kind m 1 and m 2 this measure is much easier to work with than m 1 while at least as accurate and is definitely more accurate than m 2 the upper and lower bounds of this measure are also derived and proved to be the same as those of m 1 this measure can be maximized numerically using existing explicit and systematic procedures some analytical guidelines which relate explicitly and directly the state feedback system s individual pole selection performance and decoupling to this new measure are also available and presented

a new treatment of priority first search maximum likelihood soft decision decoding of linear block codes in this correspondence we present a new method to convert the maximum likelihood soft decision decoding problem for linear block codes into a graph search problem where the generalized dijkstra s algorithm can still be applied to the decoding procedure the cost assigned to every branch in the graph is based on a generalization of the wagner rule which is an equivalent form of the maximum likelihood decoding rule the new decoding algorithm uses the properties of error patterns to reduce the search space

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

decoding linear block codes using a priority first search performance analysis and suboptimal version an efficient maximum likelihood soft decision decoding algorithm for linear block codes using a generalized dijkstra s algorithm was proposed by han hartmann and chen 1993 we prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10 sup 3 by finding an upper bound of the computational effort of the algorithm a suboptimal decoding algorithm is also proposed the performance of this suboptimal decoding algorithm is within 0 25 db of the performance of an optimal decoding algorithm for the 104 52 binary extended quadratic residue code and within 0 5 db of the optimal performance for the 128 64 binary bch code respectively

brief augmented gradient flows for on line robust pole assignment via state and output feedback this paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks first both the pole assignment and robustness requirements are appropriately formulated as two optimization problems then gradient flow models are developed for the on line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems a technique is introduced to facilitate the real time matrix inverse involved for realizing the gradient flow models the resulting augmented gradient flows have desired convergence properties simulation results are included to show the effectiveness of the proposed approach

the inertia and energy of distance matrices of complete k partite graphs abstract for a distance matrix d g its inertia is the triple of integers n d n 0 d n d where n d n 0 d n d denote the number of positive 0 negative eigenvalues of d g respectively the d energy is the sum of the absolute eigenvalues of d g in this paper we first study the inertia of distance matrices of complete k partite graphs then as applications we not only prove a conjecture proposed by caporossi et al 2009 in 5 in a different way from stevanovic et al 2013 11 but also obtain the formula of the d energy of the remaining complete k partite graphs at last we obtain the graphs with the maximum resp minimum d energy among all the complete k partite graphs with n vertices

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

on the distance spectrum of graphs abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we characterize all connected graphs with n d 2 furthermore we characterize all connected graphs of diameter 2 with exactly three d eigenvalues when 1 d is not an integer we also conjecture that the complete k partite graph is determined by its d spectrum

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

a new approach for computing the state feedback gains of multivariable systems this note presents some new results in linear systems first the relationship between the polynomial matrix description and the state space representation of multivariable systems is clarified then we show that once such a relationship is determined the coprime matrix fraction description can be easily computed and we can further develop a closed form formula to solve the pole assignment problem of multivariable systems such formula can be thought of as an extension of the ackermann s formula for mimo systems thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint

eigenvalues assignment by a particular lyapunov type equation this paper proposes a particular lyapunov type equation and uses its solution to synthesize a state feedback control such that the eigenvalues of the closed loop multiple inputs system can be assigned to the left half plane with arbitrary stability degree

robust eigenvalue assignment for generalized systems abstract in this paper we examine the problem of robust pole placement using state feedback in generalized systems we develop a robustness theory for the finite generalized spectrum of the system as a partial problem and for the infinite pole placement problem as a second partial problem where perfect conditioning is always achievable we also give bounds between the complete closed loop robust eigenvalue problem and the two partial ones the basic tool that is exploited in the presented theory is the concept of chordal metric in this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems the proposed theory is easy to implement retrieves the results for the state variable case as a special case and takes advantage of well known computational results

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

an algorithm for computing state feedback in multiinput linear systems a new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems the algorithm has good numerical behavior it also allows the user to adjust the eigenstructure of the resulting feedback system and therefore improve the condition of the problem and computation

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

the decay of stabilizability with reynolds number in a linear model of spatially developing flows this article characterizes the gradual decay of stabilizability with reynolds number in the linear complex ginzburg landau model of spatially developing ow systems when a single spatially localized actuator is used to apply the control forcing it is shown that technically the system considered is linearly stabilizable for all actuator locations at any reynolds number however as the reynolds number is increased and an increasing number of modes of the open loop system become unstable the control authority on some of these open loop unstable modes is found to be exponentially small using nite precision arithmetic and any given numerical method for computing the feedback gains an e ective upper bound on the reynolds number is reached above which it is not possible to compute a linearly stabilizing control

on graphs with near minimal distance energy abstract let g be a connected graph of order n and let d d g be its distance matrix suppose that 1 d n d are the eigenvalues of d g then de g i 1 n i d g is called the distance energy of g in this paper we characterize all connected graphs with de g 2 n 2 2 n

iterative soft input soft output decoding of reed solomon codes by adapting the parity check matrix an iterative algorithm is presented for soft input soft output siso decoding of reed solomon rs codes the proposed iterative algorithm uses the sum product algorithm spa in conjunction with a binary parity check matrix of the rs code the novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the spa is applied at each iteration the proposed algorithm can be geometrically interpreted as a two stage gradient descent with an adaptive potential function this adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and therefore significantly improves the performance simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding hdd and compare favorably with other popular soft decision decoding methods

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

the inertia and energy of the distance matrix of a connected graph abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we show that the distance matrix of a clique tree is non singular moreover we also prove that the distance matrix of a clique tree has exactly one positive d eigenvalue in addition we determine the extremal graphs with maximum and minimum distance energy among all clique trees

on a ast algorithms for decoding short linear block codes the a ast algorithm for decoding linear block codes is an efficient tree search method for decoding short linear block codes the information contained in the parity bits are potentially useful for reducing the edges needed in the tree search we propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits analysis for the number of required message bits for obtaining sums of parity bits is provided the information contained in the parity bits can help to reduce the number of search tree edges

a decoding of block codes the a algorithm is applied to maximum likelihood soft decision decoding of binary linear block codes this paper gives a tutorial on the a algorithm compares the decoding complexity with that of exhaustive search and viterbi decoding algorithms and presents performance curves obtained for several codes

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes

maximal stability robustness for state equations a measure for stability robustness of a linear time invariant finite dimensional system state equations is introduced an upper bound for the measure is derived using the characteristic values of the system it is shown that the set of optimal systems namely systems for which the stability robustness measure attains the bound contains the normal set which has been considered as the set of optimal robustness

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems