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

optimal l sub spl infin to l sub spl infin estimation for periodic systems in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l sub spl infin of the estimation error in the case of linear periodically time varying systems subjected to unknown but magnitude bounded l sub spl infin inputs these inputs consist of process and observation noises and the optimization problem is considered over an infinite time horizon lifting techniques are utilized to transform the problem to a time invariant l sub 1 model matching problem subject to additional constraints taking advantage of the particular structure of the estimation problem it is shown how standard methods of l sub 1 optimization in particular the delay augmentation technique can be suitably modified to solve this nonstandard problem

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

a class of collocation methods for numerical integration of initial value problems for the numerical solution of initial value problems a general procedure to determine global integration methods is derived and studied they are collocation methods which can be easily implemented and provide a high order accuracy they further provide globally continuous differentiable solutions computation of the integrals which appear in the coefficients are generated by a recurrence formula and no integrals are involved in the calculation numerical experiments provide favorable comparisons with other existing methods

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

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

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

robust stability and performance via fixed order dynamic compensation two robust control design problems are considered the robust stabilization problem in volves deterministically modeled bounded butunknown time varying parameter variations while the robust performance problem includes in addition a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations for both problems the design goal is a fixed order i e reduced or full order dynamic strictly proper feedback compensator a sufficient condition for solving the robust stabilization problem is given by means of a quadratic lyapunov function parameterized by the compensator gains for the robust performance problem the lyapunov function provides an upper bound for the closed loop performance this leads to consideration of the auxiliary minimization problem minimize the performance bound over the class of fixed order controllers subject to the lyapunovofunction constraint necessary conditions for optimality in the auxiliary problem thus serve as sufficient conditions for robust stability and performance in the original problem two particular bounds are considered for constructing the quadratic lyapunov function the first corresponds to a right shift multi plicative white noise model while the second was suggested by recent work of petersen and hollot the main result is an extended version ofthe optimal projection equations for fixed order dynamic compensation whose solutions are guaranteed to provide both robust stability and robust performance

analysis of a family of chebyshev methods for y f x y abstract methods proposed by panovsky and richardson this journal 1988 are interpreted as a family of symmetric two step hybrid methods each method is based on a polynomial interpolant of degree n for y for which the nodes are determined by the extrema of the chebyshev polynomial of degree n it is shown that the order of accuracy is n 1 for odd n and n 2 for even n and expressions for the local error constants are given the stability properties of each method are determined by the roots of a quadratic equation 2 2 n 1 0 where n 2 is a rational approximation for cos the intervals of periodicity which are also intervals of absolute stability are tabulated for n 10 numerical examples provide comparisons with other methods

a robust periodic pole assignment algorithm in this note a robust periodic pole assignment algorithm is proposed for linear time invariant discrete time systems the condition numbers of the eigenvector matrices of the closed loop system are assumed as a robustness measure and a periodic state feedback law is deduced by the minimization of the condition numbers associated to the eigenvectors of the monodromy matrix of the closed loop system the proposed periodic pole assignment algorithm has been tested on a number of examples giving satisfactory results

on convergence and bias correction of a joint estimation algorithm for multiple sinusoidal frequencies twenty years ago kay proposed an iterative filtering algorithm ifa for jointly estimating the frequencies of multiple complex sinusoids from noisy observations ifa is based on the fact that the noiseless signal is an autoregressive ar process so the frequency estimation problem can be reformulated as the problem of estimating the ar coefficients by iterating the cycle of ar coefficient estimation and ar filtering ifa provides a computationally simple procedure yet capable of accurate frequency estimation especially at low signal to noise ratio snr however the convergence of ifa has not been established beyond simulation and a very special case of a single frequency and infinite sample size this article provides a statistical analysis of the algorithm and makes several important contributions it shows that the poles of the ar filter must be reduced by an extra shrinkage parameter to accommodate poor initial values and avoid being trapped into false solutions it also shows that the ar estima

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

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

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

estimation of the parameters of sinusoidal signals in non gaussian noise accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications in this paper the problem is investigated under the assumption of non gaussian noise in general and laplace noise in particular it is proven mathematically that the maximum likelihood estimator derived under the condition of laplace white noise is able to attain an asymptotic cramer rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares it is also proven that when applied to non laplace situations the laplace maximum likelihood estimator which may also be referred to as the nonlinear least absolute deviations estimator can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails a computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function simulation results are provided to validate the analytical findings

the development of variable step symplectic integrators with application to the two body problem the authors develop and test variable step symplectic runge kutta nystrom algorithms for the integration of hamiltonian systems of ordinary differential equations numerical experiments suggest that for symplectic formulae moving from constant to variable stepsizes results in a marked decrease in efficiency on the other hand symplectic formulae with constant stepsizes may outperform available standard nonsymplectic variable step codes for the model situation consisting in the long time integration of the two body problem our experimental findings are backed by theoretical analysis

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

modeling of parameter variations and asymptotic lqg synthesis conventional approaches in modern robustness and sensitivity theory are not adequate for the problems associated with parameter variation since the structure of parameter variations cannot be modeled properly or included in the synthesis procedure a new modeling technique is proposed to handle a class of structured plant uncertainties in a direct way the key is to treat deterministic parameter variations as an internal feedback loop so that the structure of parameter variations is embedded in its model an asymptotic lqg design synthesis based on this modeling method is also presented an important relationship between the structure of plant uncertainties and the lqg weighting matrices is obtained this relationship clearly specifies the kind of parameter variations allowable for the lqg ltr method

pole placement by parametric output feedback abstract this note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m p n where n m and p are the number of states inputs and outputs respectively the approach is based upon parametric eigenstructure assignment of linear time invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations thus the resulting analytical solution explicitly offers all remaining m p n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping minimizing the norm of the feedback matrix and robust control respectively

high performance state feedback robust and output feedback stabilizing control a systematic design algorithm improves a fundamentally new design approach which can generally realize the robustness properties of the state feedback control for the first time by guaranteeing the resulting feedback system stability to the best of the authors knowledge this improved design also provides the first simple and systematic design procedure and design solution to the strong stabilization problem stabilize feedback system by a stable output feedback compensator finally high performance high robustness and low controller order can all be systematically achieved by this design

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

linear quadratic gaussian synthesis with reduced parameter sensitivity we present a method for improving the tolerance of a conventional lqg controller to parameter errors in the plant model the improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the lqr cost function and also the process and measurement noise models adjusting the sizes of these additional terms permits a trade off between robustness and nominal performance manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers conditions are developed under which the high gain approach asymptotically recovers the robustness of the corresponding full state feedback design and the low gain approach makes the closed loop poles asymptotically insensitive to parameter errors

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

mixed collocation methods for y f x y inline equatio abstract the collocation methods introduced here are based on linear combinations of trigonometric functions and powers the motivation is to provide better approximations for oscillatory solutions of initial value problems for differential equations of the special form y f x y the resulting methods for two or more collocation points are implicit runge kutta nystrom methods with coefficients which depend on both the fitted angular frequency and the steplength algebraic and trigonometric order conditions are considered and the stability properties of some methods are examined particular mixed collocation methods and other methods for the same class of problems are compared by applying them to a variety of test problems

least squares pole assignment by memoryless output feedback in this paper a pole assignment problem for a linear time invariant control system by memoryless output feedback is posed as a least squares optimisation problem and analysed the cost functions are appropriately modified so as to obtain convergence of the corresponding gradient flow and existence of the global minimum this approach is also extended to accommodate the output pole assignment problem with insensitivity against disturbances in system parameters the relation between the modified cost functions and the original pole assignment problem is revealed the proposed approach is compared with other existing approaches and illustrated by numerical results

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

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

maximum likelihood estimation of multiple frequencies with constraints to guarantee unit circle roots an approximate maximum likelihood estimator mle of multiple exponentials converts the frequency estimation problem into a problem of estimating the coefficients of a z polynomial with roots at the desired frequencies theoretically the roots of the estimated polynomial should fall on the unit circle but mle as originally proposed does not guarantee unit circle roots this drawback sometimes causes merged frequency estimates especially at low snr if all the sufficient conditions for the z polynomial to have unit circle roots are incorporated the optimization problem becomes too nonlinear and it loses the desirable weighted quadratic structure of mle in the present paper the exact constraints are imposed on each of the first order factors corresponding to individual frequencies for ensuring unit circle roots the constraints are applied during optimization alternately for each frequency in the absence of any merged frequency estimates the rms values more closely approach the theoretical cramer rao cr bound at low snr levels

nearly singular filtering for uniform and non uniform rank linear continuous systems abstract the problem of the minimum variance stationary estimation of linear time invariant continuous systems is considered in the case where the norm of tho measurement white noise intensity approaches zero solutions in closed form are obtained for the kalman gain and the corresponding minimum error covariance matrix of the filtered estimate in terms of the noise intensity norm and the system transfer function matrix both uniform and non uniform rank systems are considered and for the first time a solution is obtained for the case where the infinite zeros of the system tond to infinity with multiple rates

an explicit runge kutta nystro m method is canonical if and only if its adjoint is explicit canonical runge kutta nystrom methods for hamiltonian dynamical systems are considered these systems arise in various areas in the physical sciences canonical methods preserve certain properties of the system in this paper it is shown that an explicit runge kutta nystrom method is canonical if and only its adjoint is explicit the adjoint of a method is obtained by time reversal one application for this result and other results in this paper is that if an explicit canonical runge kutta nystrom method of odd order is concatenated with its adjoint the result is an explicit canonical method of one order higher

on the recovery procedure for lqg systems abstract the loop transfer function recovery ltr procedure of doyle and stein 1979 ieee trans aut control ac 24 607 611 is re examined in the context of singular measurement lqg systems using existing closed form expressions for singular optimal estimation an alternative proof of the ltr is presented some of the structural properties of the ltr are obtained naturally using this approach it is shown that in the limit the control effort becomes infinite and therefore the critical tradeoff is between control effort and robustness

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

maximum likelihood estimation of superimposed complex sinusoids in white gaussian noise by reduced effort coarse search recs an efficient implementation for the maximum likelihood estimator for the frequencies of superimposed complex sinusoids in white gaussian noise is presented the algorithm uses one dimensional searches and classical optimization techniques and produces data that can be used for model order selection its convergence and statistical properties are verified through simulation the method does not require polynomial rooting frequent manipulation of large matrices or the use of approximate constraints

statistical analysis of pisarenko s method for sinusoidal frequency estimation statistical analysis is performed for pisarenko s method of sinusoidal frequency estimation by using the periodogram technique under the assumption that the data consist of several sinusoids plus white noise we give an asymptotic expression of the error variance of the sinusoidal frequency estimator also a modified method is proposed this is computationally efficient but the statistical property is not improved we also present simulation results and compare them to the theoretical ones lastly we point out that the pisarenko s method can be implemented as an on line bias compensated least squares algorithm thus avoiding the eigenvalue and eigenvector calculations

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

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

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

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

on the robustness of lq regulators it is shown that in spite of its large gain and phase margins the linear quadratic state feedback regulator may suffer from poor robustness where small changes in the parameters of the system may lead to fast unstable closed loop modes

author s reply to comments on the loop transfer recovery the author disagrees with the two comments made in the above paper by rachid ibid vol 40 no 2 1995 on the new loop transfer recovery ltr technique proposed by the author ibid vol ac 32 no 9 1987 1 the technique could lead to poor results and 2 the technique cannot be applied to nonminimum phase systems referring to the first comment it is pointed out that the new technique can yield exact solutions for all plants with more than inputs or with at least one stable transmission zero the author dismisses the second as incorrect

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

robustness bound for receding horizon finite memory control lyapunov krasovskii approach this article presents a robustness bound rb of receding horizon finite memory control rhfmc kwon w h and han s 2004 receding horizon finite memory controls of output feedback controls for state space systems ieee transactions on automatic control 49 1905 1915 for continuous time state space systems with norm bounded uncertainties the proposed rb is easily obtained by solving a convex problem in terms of a linear matrix inequality we show through a numerical example that the rhfmc can guarantee the robust stabilisation for a larger class of uncertain systems than linear quadratic gaussian controls when some poles of closed loop systems are close to an imaginary axis in the complex plane

a fast maximum likelihood algorithm for frequency estimation of a sinusoid based on newton s method a fast algorithm to estimate the frequency of a sinusoid is presented here it is based on newton s method for finding the root of an equation and it is shown that under easily met conditions the root mean square error rmse of the estimator is practically equal to the cramer rao bound after only two iterations of newton s method for all signal to noise ratios snr s above threshold the estimator s probability density function is computed analytically and the rmse is calculated for one and two iterations of newton s method its computational load is shown to be significantly less than other conventional algorithms

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

a family of implicit chebyshev methods for the numerical integration of second order differential equations abstract a family of implicit methods based on intra step chebyshev interpolation is developed for the solution of initial value problems whose differential equations are of the special second order form y f y x x the general procedure allows stepsizes which are considerably larger than commonly used in conventional methods computation overhead is comparable to that required by high order single or multistep procedures in addition the iterative nature of the method substantially reduces local errors while maintaining a low rate of global error growth

asymptotic analysis of a fast algorithm for efficient multiple frequency estimation based on an asymptotic analysis of the contraction mapping cm method of li and kedem 1993 a bandwidth shrinkage rule is proposed for fast and accurate estimation of the frequencies of multiple sinusoids from noisy measurements the cm frequency estimates are defined as the fixed points of a contractive mapping formed by the lag one autocorrelation coefficient calculated from the output of a parametric filter applied to the observed time series with bandwidth parameters judiciously chosen according to the asymptotic analysis the algorithm is shown to be able to accommodate possibly poor initial values of precision o n sup 1 3 and converge to a final estimate whose accuracy is arbitrarily close to o n sup 3 2 the optimal error rate for frequency estimation under the gaussian assumption the total computational complexity of the algorithm is shown to be o n log n which is comparable to that of n point fast fourier transform fft a novelty in the asymptotic analysis is that it accommodates closely spaced frequencies by allowing not only the filter bandwidth but also the frequency separation to be functions of the sample size n this enables an assessment of the accuracy of the frequency estimates for given bandwidths and initial values in situations where some or all of the frequencies are close to each other

sensitivity properties of multirate feedback control systems based on eigenstructure assignment some sampled data systems e g fly by wire control schemes have a necessarily multirate structure various input and or outputs sampled at different rates when considering a multirate system which has parameter uncertainty it is important to examine ways in which the full freedom of the multivariable design can be utilized to minimize the sensitivity to parameter variations given the accompanying problems induced by intersample ripple disturbance this note examines the design capabilities of a class of multirate systems with multiple input and fixed state sampling rates mifs based on eigenstructure assignment although the use of eigenstructure assignment for continuous and single rate discrete systems is well understood the eigenstructure assignment for the design of multirate feedback systems is an open topic of research accepting that the problems of intersample ripple are often magnified through multirate control there are advantages in terms of increased freedom for minimizing sensitivity and optimizing robustness to parameter variations a special feature of the mifs class of multirate systems is the ability to introduce extra design freedom in the eigenproblem by a suitable choice of eigenstructure assignment and sample rates the criteria for the selection of minimum sample rates to produce this extra freedom and the implication that this has on the eigenstructure assignment problem are outlined the improved insensitivity properties are demonstrated using an example comparing the performance of multirate and corresponding single rate designs

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

robustness in partial pole placement the robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined the projection procedure gives a reduced order pole assignment problem it is shown that the sensitivities of the assigned poles in the complete closed loop system are bounded in terms of the sensitivities of the assigned reduced order poles and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open loop poles if the assigned poles are well separated from the unaltered poles these bounds are expected to be tight the projection procedure is described in 3 and techniques for finding robust or insensitive solutions to the reduced order problem are given in 1 2

the chebyshev methods of panovsky and richardson as runge kutta nystro m methods abstract the two step methods proposed by panovsky and richardson this journal 1988 and analysed by coleman and booth this journal 1992 are shown to be equivalent to certain runge kutta nystrom methods for differential equations of the form y f x y an important advantage of the new formulation is that it is no longer necessary to provide additional starting values at the beginning of a calculation or when the steplength or the order is changed the new formulation is also more stable with respect to the propagation of rounding errors

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

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

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

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

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

an iterative method for exact maximum likelihood estimation of the parameters of a harmonic series a procedure is described for determining the exact maximum likelihood ml estimates of the parameters of a harmonic series i e the fundamental frequency and the amplitude and phase of each harmonic existing ml methods are only approximate in the sense that terms present due to mixing between the harmonics are ignored these terms asymptotically reduce to zero as the sample size increases to infinity it is argued that these terms can be significant for short signal lengths the application of the expectation maximization algorithm results in an iterative procedure that converges to a stationary point on the true parameter likelihood surface if global convergence results this point yields the exact ml estimates simulation studies illustrate the advantages of the method when short data lengths are used

on the stability robustness of the continuous time lqg optimal control the robustness properties of the lqg optimal controller that is obtained by the asymptotic recovery method are discussed it is shown that in spite of the good recovered stability margins the resulting closed loop design is inherently unrobust in the sense that small parameter variations in the plant and or small realization errors in the controller may lead to an instantaneous instability of the design

the lqg optimal regulation problem for systems with perfect measurements explicit solution properties and application to practical designs the continuous time stationary linear quadratic gaussian lqg optimal regulation problem is considered where the measurements are free of white noise components a simple direct solution in the s domain is derived for the optimal controller for general linear time variant right invertible or left invertible systems the explicit expressions that are found for the controller transference and for the regulator return ratio matrix can be used to obtain a practical suboptimal design in the s domain these expressions are applied to derive simple conditions for the precise recovery of the return ratio matrix of the lqg regulator

on preserving the robustness of an optimal control system with observers a new simple and general method is proposed in this note to preserve the robustness of the lq control system which involves state estimators the method is to minimize the estimator gain to the system input by selecting the estimator poles while the existing method is to maximize the estimator gain to the system output by introducing additional noise in the system input noise description an example demonstrates that the stability margin of the feedback system with the estimator designed by this method is even better than that of a system without the estimators

newton algorithms for conditional and unconditional maximum likelihood estimation of the parameters of exponential signals in noise the authors present polynomial based newton algorithms for maximum likelihood estimation mle of the parameters of multiple exponential signals in noise this formulation can be used in the estimation for example of the directions of arrival of multiple noise corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise corrupted complex sine waves the algorithms offer rapid convergence and exhibit the computation efficiency associated with the polynomial approach compact closed form expressions are presented for the gradients and hessians various model assumptions concerning the statistics of the underlying signals are considered numerical simulations are presented to demonstrate the algorithms performance

on frequency estimation summary t this paper discusses a least squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series it is shown that the usual asymptotics on estimation of frequency amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective computational issues are discussed and some illustrations are provided bolt brillinger 1979 make use of these asymptotic results we consider a time series model of the form x a cos wt f e where e is a stationary noise sequence and one is interested in estimating the amplitude frequency and phase of the harmonic component the asymptotic theory of the least squares estimates of these parameters has a long history whittle 1951 1953 obtained some of the earliest results more recent results are by hasan 1982 hannan 1973 and walker 1971 who formalize and extend whittle s results in these works it is shown that the asymptotic variance of the frequency estimate is of order n 3 and that the asymptotic variances of the other two components are of the more usual order n these results extend when there are several harmonic components the rate for the estimate of w seems almost unbelievably good and our work was motivated by a desire to see how reliable the asymptotic theory is in brief we find that the product of the amplitude and the sample size n must be quite large in order for the asymptotic theory to be meaningful if this product is not large the frequency estimate is much more variable than indicated by the asymptotic theory and the amplitude estimate is severely biased in applications in which the amplitude is small giving rise to a small peak in the periodogram these results suggest that naive application of the asymptotic theory to gauge resolution can be quite misleading section 2 of this paper is devoted to a review and examination of the asymptotic theory we are also concerned with computational issues arising from the least squares problem this problem is nonlinear in the parameters so that some sort of iterative search must be employed typically search methods start from an initial guess and then proceed by a sequence of modified newton raphson steps for this nonlinear least squares problem it turns out that there are many local minima with a separation in frequency about n l which makes the stationary point to which the iterative scheme converges extremely sensitive to the starting values and this problem gets worse as the sample size increases furthermore it follows from the results of 2 that the estimate of the amplitude is very biased unless the frequency is resolved with order o n so that failure to converge to the global minimum may give a very poor estimate of amplitude the problem becomes

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

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

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

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

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

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

variable step size does not harm second order integrators for hamiltonian systems abstract experiments have shown that variable step size degrades some symplectic integrators for certain hamiltonian systems in particular for the two body problem in this paper we show that the error growth in time for variable step size symplectic is not in general quadratic we demonstrate this by applying several integrators to the two body problem the error growth in time in the case of the second order integrators symplectic or nonsymplectic turns out to be approximately linear

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

a complete analytical solution to the equation ta ft lc and its applications in this note a complete analytical and restriction free solution with complete and explicit freedom of the matrix equation ta ft lc is proposed here a c is given and is observable and f is in the jordan form with arbitrary given eigenvalues this solution appears to be new because it can be applied directly to obtain significantly better solutions to the following three basic design problems 1 2 d system eigenvalue assignment 2 function observer design and 3 state feedback eigenstructure design as shown in this note

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

on the robustness of meop design versus asymptotic lqg synthesis an analysis is presented of generalized lqg linear quadratic gaussian type algorithms with regard to robustness characteristics comparisons are made of the maximum entropy optimal projection meop methodology versus the linear quadratic gaussian with loop transfer recovery lqg ltr technique and the parametric robust linear quadratic gaussian synthesis procedure the performance of a reduced order direct controller design is compared with the full order designs on a example representative of typical flexible structure dynamics