optimal h model reduction via linear matrix inequalities continuous and discrete time cases necessary and sufficient conditions are derived for the existence of a solution to the continuous time and discrete time h model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set in addition an explicit parametrization of all reduced order models that correspond to a feasible solution is provided in terms of a contractive matrix these results follow from the recent solution of the h control design problem using lmis particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth order h approximation problem and the convexity of this problem is demonstrated computational issues are discussed and an iterative procedure is proposed to solve the h model reduction problem using alternating projections although global convergence of the algorithm is not guaranteed

approximation based adaptive fuzzy tracking control for a class of nonstrict feedback stochastic nonlinear time delay systems this paper focuses on the problem of approximation based adaptive fuzzy tracking control for a class of stochastic nonlinear time delay systems with a nonstrict feedback structure a variable separation approach is introduced to overcome the design difficulty from the nonstrict feedback structure mamdani type fuzzy logic systems are utilized to model the unknown nonlinear functions in the process of controller design and an adaptive fuzzy tracking controller is systematically designed by using a backstepping technique it is shown that the proposed controller guarantees that all signals in the closed loop system are fourth moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results are provided to demonstrate the effectiveness of our results further developments will consider how to generalize the proposed strategy to nonstrict feedback nonlinear systems with input nonlinearities

reduced order generalized h_ infty filtering for linear discrete time systems with application to channel equalization this paper investigates the problem of reduced order generalized h infty filtering for linear discrete time systems generalized h infty filtering covers standard h infty filtering as a special case and can make use of the frequency domain characteristics of practical signals moreover reduced order filters are more attractive than full order ones regarding implementability by virtue of the generalized bounded real lemma a new necessary and sufficient condition is proposed for analyzing the generalized h infty performance of the filtering error system to compute reduced order generalized h infty filters a necessary and sufficient condition is then derived in terms of matrix inequalities to solve which iterative linear matrix inequality algorithms are further developed in addition the proposed filter design method is applied to cope with the channel equalization problem examples are finally presented for illustrating the proposed method

adaptive fault tolerant stabilization for nonlinear systems with markovian jumping actuator failures and stochastic noises in this paper we consider the fault tolerant stabilization problem for a class of nonlinear systems with uncertain parameters uncertainties caused by markovian jumping actuator failures and stochastic noises are also taken into consideration different from most existing results the number of actuator failures may be infinite and stochastic functions related to multi markovian variables have been introduced to denote the failure scaling factors for the actuators which is practical but challenging three main difficulties arise first is how to establish fundamentals for systems involving multi markovian variables and stochastic noises including the joint transition probability the infinitesimal generator the existence and uniqueness of the solution and so on second is how to handle the extra transition rate related terms appearing in the infinitesimal generator of the lyapunov function last is how to cope with the involved higher order hessian term in the ito stochastic differentiation by proposing a new adaptive fault tolerant control scheme the boundedness in probability of all the closed loop signals has been ensured an example of altitude fault tolerant control for a generic hypersonic air vehicle is presented to show the effectiveness of the proposed scheme

weighted hankel norm approximation calculation of bounds abstract frequency domain bounds are computed for the approximation error involved in the optimum hankel norm approximation procedure the bounds differ from those arising in the unweighted optimal hankel norm approximation procedure by a multiplicative factor depending solely on the weighting function this factor becomes unity when the weighting function is constant

adaptive fuzzy backstepping output feedback tracking control of mimo stochastic pure feedback nonlinear systems with input saturation abstract in this paper the adaptive fuzzy backstepping output feedback tracking control problem is considered for a class of uncertain stochastic multi input and multi output mimo nonlinear systems in pure feedback form the stochastic mimo nonlinear systems under study have unknown nonlinear functions input saturation and immeasurable states by using fuzzy logic systems to identify the uncertain nonlinear system and a smooth function to approximate the input saturation a fuzzy state observer is designed and the estimations of the immeasurable states are obtained based on the backstepping recursive design technique an adaptive fuzzy output feedback tracking control approach is developed it is shown that the proposed control approach guarantees that all the signals of the resulting closed loop system are semi globally uniformly ultimately bounded sguub in mean square in the sense of probability and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately a simulation example is provided to show the effectiveness of the proposed approach

sliding mode control design for nonlinear systems using probability density function shaping in this paper we propose a sliding mode based stochastic distribution control algorithm for nonlinear systems where the sliding mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function kullback leibler divergence is introduced to the stochastic distribution control and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode it is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank condition which is much weaker than the persistent excitation condition the effectiveness of the proposed algorithm is illustrated by simulation

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

adaptive neural control for a class of stochastic nonlinear systems by backstepping approach this paper addresses adaptive neural control for a class of stochastic nonlinear systems which are not in strict feedback form based on the structural characteristics of radial basis function rbf neural networks nns a backstepping design approach is extended from stochastic strict feedback systems to a class of more general stochastic nonlinear systems in the control design procedure rbf nns are used to approximate unknown nonlinear functions and the backstepping technique is utilized to construct the desired controller the proposed adaptive neural controller guarantees that all the closed loop signals are bounded and the tracking error converges to a sufficiently small neighborhood of the origin two simulation examples are used to illustrate the effectiveness of the proposed approach

dynamics modeling and tracking control of robot manipulators in random vibration environment in this technical brief the problem of modeling and tracking control for the manipulator with multi revolute joints in random vibration environment is considered by analyzing the effect of environment to the mass points and introducing an equivalent stochastic noise process a stochastic hamiltonian dynamic model is constructed to describe the motion of the manipulator based on the constructed model a state feedback backstepping controller in vector form is designed such that the unique solution of the closed loop system is bounded in probability and the mean square of the tracking error converges to an arbitrarily small neighborhood of zero

adaptive neural tracking control for stochastic nonlinear strict feedback systems with unknown input saturation in this paper the problem of adaptive neural tracking control is considered for a class of single input single output siso strict feedback stochastic nonlinear systems with input saturation to deal with the non smooth input saturation nonlinearity a smooth nonaffine function of the control input signal is used to approximate the input saturation function classical adaptive technique and backstepping are used for control synthesis based on the mean value theorem a novel adaptive neural control scheme is systematically derived without requiring the prior knowledge of bound of input saturation it is shown that under the action of the proposed adaptive controller all the signals of the closed loop system remain bounded in probability and the tracking error converges to a small neighborhood around the origin in the sense of mean quartic value two simulation examples are provided to demonstrate the effectiveness of the presented results

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

an ilc based adaptive control for general stochastic systems with strictly decreasing entropy in this paper a new method for adaptive control of general nonlinear and non gaussian unknown stochastic systems has been proposed the method applies the minimum entropy control scheme to decrease the closed loop randomness of the output under an iterative learning control ilc basis both modeling and control of the plant are performed using dynamic neural networks for this purpose the whole control horizon is divided into a certain number of time domain subintervals called batches and a pseudo d type ilc law is employed to train the plant model and controller parameters so that the entropy of the closed loop tracking error is made to decrease batch by batch the method has the advantage of decreasing the output uncertainty versus the advances of batches along the time horizon the analysis on the proposed ilc convergence is made and a set of demonstrable experiment results is also provided to show the effectiveness of the obtained control algorithm where encouraging results have been obtained

improved results on h model reduction for markovian jump systems with partly known transition probabilities abstract this paper is concerned with the model reduction problem for markovian jump systems with partly known transition probabilities by making use of an existing result on the convex properties of the transition probabilities an improved condition is first derived for the h performance analysis of the error system two different approaches one in terms of linear matrix inequalities lmis and another in the form of an iterative algorithm subject to lmi constraints are then proposed to find a reduced order model such that the h performance of the error system is bounded by a specified level the first approach is obtained using finsler s lemma and involves fewer decision variables than the existing method it is shown that the proposed methods cover some existing results as special cases finally the advantages of our results are clearly illustrated by a numerical example

h sub spl infin model reduction with application to flexible systems in this note h sub spl infin model reduction of continuous time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method leading to the conclusion that the proposed method performs significantly better finally the proposed method is applied to the determination of a reduced order model of a flexible bar

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

adaptive output neural network control for a class of stochastic nonlinear systems with dead zone nonlinearities this paper investigates the problem of adaptive output neural network nn control for a class of stochastic nonaffine and nonlinear systems with actuator dead zone inputs first based on the intermediate value theorem a novel design scheme that converts the nonaffine system into the corresponding affine system is developed in particular the priori knowledge of the bound of the derivative of the nonaffine and nonlinear functions is removed then by employing nns to approximate the appropriate nonlinear functions the corresponding adaptive nn tracking controller with the adjustable parameter updated laws is designed through a backstepping technique furthermore it is shown that all the closed loop signals are bounded in probability and the system output tracking error can converge to a small neighborhood in the sense of a mean quartic value finally experimental simulations are provided to demonstrate the efficiency of the proposed adaptive nn tracking control method

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

adaptive output feedback tracking of stochastic nonlinear systems we address the adaptive stabilization and tracking problems for a class of output feedback canonical systems driven by wiener noises of unknown covariance filtered transformation and backstepping techniques are employed in the stochastic control design we obtain two adaptive controllers that guarantee the global stability in probability for vanishing perturbations or the input to state stability in probability for nonvanishing perturbations respectively the tracking error can converge to a small residual set around the origin in the sense of mean quartic value

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

a new frequency weighted balanced truncation method and an error bound in this paper a new frequency weighted model reduction method with an a priori error bound is proposed the method is a generalization of enns technique 1984 and yields stable models even when both input and output weightings are included the proposed method is compared with other existing methods using numerical examples

theory of matching rules for the 3 dimensional penrose tilings we consider packings of the two ammann rhombohedra used for tiling the three dimensional space we define decorations for the facets of the rhombohedra using elementary algebraic topology we prove that any tiling by these rhombohedra with matching decorations is a quasiperiodic penrose tiling the proof does not involve any reference to self similarity

approximation of fir by iir digital filters an algorithm based on balanced model reduction an algorithm for the approximation of finite impulse response fir filters by infinite impulse response iir filters is presented the algorithm is based on a concept of balanced model reduction the matrix inversions normally associated with this procedure are notoriously error prone due to ill conditioning of the special matrix forms required this difficulty is circumvented here by directly formulating a reduced state space system description which is input output equivalent to the system that would more conventionally be obtained following the explicit step of constructing an interim balanced realization examples of fir by iir filter approximations are included

design of delta sigma modulators via generalized kalman yakubovich popov lemma this paper is concerned with the design of delta sigma modulators via the generalized kalman yakubovich popov lemma the shaped noise transfer function ntf is assumed to have infinite impulse response and the optimization objective is minimizing the maximum magnitude of the ntf over the signal frequency band by virtue of the gkyp lemma the optimization of an ntf is converted into a minimization problem subject to quadratic matrix inequalities and then an iterative algorithm is proposed to solve this alternative minimization problem each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages moreover specifications on the ntf zeros are also integrated in the design method a design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal to noise ratio

ilc based fixed structure controller design for output pdf shaping in stochastic systems using lmi techniques in this paper a generalized state space controller design for the shaping of the output probability density function pdf is presented for non gaussian dynamical stochastic systems a radial basis function rbf neural network is used to approximate the output pdf of the system such a neural network consists of a number of weights and corresponding basis functions using such an approximation the dynamics of the original stochastic system can be expressed as the dynamics between the control input and the weights of the rbf neural network the task of output pdf control can therefore be reduced to a rbf weight control together with an adaptive tuning of the basis function parameters i e the centers and widths of the basis functions to achieve this aim the control horizon is divided into certain intervals hereinafter called batches using these definitions the whole control strategy consists of three stages namely a sub space parameter identification of the dynamic nonlinear model that relates the control signal to the weights of the rbf neural network b weight tracking controller design using an lmi based convex optimization technique and c rbf basis functions shape tuning in terms of their centers and widths using an iterative learning control ilc framework among the above stages the first two are performed within each batch while stage c is carried out between any two adjacent batches such an algorithm has the advantage of the batch by batch improvement of the closed loop output pdf tracking performance moreover the controller mentioned in stage b is a general controller in a state space form stability analysis has been performed and simulation results are included to show the effectiveness of the proposed method where encouraging results have been made

design of low order linear phase iir filters via orthogonal projection this paper presents an indirect linear phase iir filter design technique based on a reduction of linear phase fir filters the desired filter is obtained by minimizing the l sub 2 norm of the difference between the original fir filter and the lower order iir filter we first establish a relationship between the hankel singular values of the discarded part of the fir filter and the l sub 2 norm of the corresponding filter approximation error based on model truncation this result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation bt and the impulse response gramian irg methods we then develop an iterative algorithm for finding an optimal iir filter based on a matrix projection of the original fir filter the convergence of the proposed algorithm is established filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband numerical examples show that the proposed algorithm offers the best performance

active disturbance rejection control approach to output feedback stabilization of a class of uncertain nonlinear systems subject to stochastic disturbance the active disturbance rejection control adrc is now considered as a powerful control strategy in dealing with large uncertainty covering unknown dynamics external disturbance and unknown part in coefficient of the control however all theoretical works up to present are limited to deterministic uncertainty in this technical note we generalize the adrc to uncertain nonlinear systems subject to external bounded stochastic disturbance described by an uncertain stochastic differential equation driven by white noise we first design an extended state observer eso that is used to estimate both state and total disturbance which includes the internal uncertain nonlinear part and the external uncertain stochastic disturbance it is shown that the resulting closed loop system is practically stable in the mean square topology the numerical experiments are carried out to illustrate effectiveness of the proposed approach

adaptive fuzzy tracking control for a class of pure feedback stochastic nonlinear systems with non lower triangular structure this paper considers the problem of the adaptive fuzzy tracking control for a class of nonaffine stochastic nonlinear systems without lower triangular form by using fuzzy logic systems universal approximation property an adaptive fuzzy controller is proposed which guarantees that all the signals in the closed loop system are bounded in the sense of mean quartic value and the output tracking error eventually converges to a small neighborhood around the origin simulation results are provided to illustrate the effectiveness of the proposed scheme

iir approximation of fir filters via discrete time vector fitting we present a novel technique for approximating finite impulse response fir filters with infinite impulse response iir structures through extending the vector fitting vf algorithm used extensively for continuous time frequency domain rational approximation to its discrete time counterpart called vfz vfz directly computes the candidate filter poles and iteratively relocates them for progressively better approximation each vfz iteration consists of the solutions of an overdetermined linear equation and an eigenvalue problem with real domain arithmetic to accommodate complex poles pole flipping and maximum pole radius constraint guarantee stability and robustness against finite precision implementation comparison against existing algorithms confirms that vfz generally exhibits fast convergence and produces highly accurate iir approximants

on convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems in this paper the practical mean square convergence of active disturbance rejection control for a class of uncertain stochastic nonlinear systems modelled by the ito type stochastic differential e

robust model reduction of uncertain systems maintaining uncertainty structure this article presents a new approach for or robust model reduction for uncertain systems based on an optimisation algorithm applied directly in the space of reduced order model parameters the proposed approach can be applied to both polytopic or affine parameter dependent models as well as for continuous or discrete time systems the developed procedure is capable of computing both fixed reduced order model as well as uncertain reduced order model keeping the original uncertainty structure the resulting reduced order model is guaranteed to be robust stable

model reduction based on regional pole and covariance equivalent realizations in this paper a novel model reduction problem is studied for linear continuous time time invariant stochastic systems the purpose of this problem is to design the reduced order model so that it has the same dominant pole region and steady state output covariance as those of the original full order model the resulting reduced order model can approximate the corresponding original full order model in two important aspects i e transient and steady state performances necessary and sufficient conditions for the existence of desired reduced order models are established and an explicit expression for these reduced order model is also presented an illustrative example is used to demonstrate the effectiveness of the proposed design method

a survey of model reduction by balanced truncation and some new results balanced truncation is one of the most common model reduction schemes in this note we present a survey of balancing related model reduction methods and their corresponding error norms and also introduce some new results five balancing methods are studied 1 lyapunov balancing 2 stochastic balancing 3 bounded real balancing 4 positive real balancing and 5 frequency weighted balancing for positive real balancing we introduce a multiplicative type error bound moreover for a certain subclass of positive real systems a modified positive real balancing scheme with an absolute error bound is proposed we also develop a new frequency weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians two numerical examples are illustrated to verify the efficiency of the proposed methods

absence of weak local rules for the planar quasicrystalline tiling with the 8 fold rotational symmetry levitov s theory of local rules the preceding paper of this issue gives no prediction for the planar quasicrystalline tiling having 8 fold rotational symmetry absence of weak local rules for this particular tiling is proven

technical communique h model reduction for uncertain switched linear discrete time systems in this paper the problem of h model reduction for switched linear discrete time systems with polytopic uncertainties is investigated a reduced order switched model is constructed for a given robustly stable switched system which has the same structural polytopic uncertainties as the original system such that the resulting error system is robustly asymptotically stable and an h error performance is guaranteed a sufficient condition for the existence of the desired reduced order model is derived and formulated in terms of a set of linear matrix inequalities by solving the corresponding convex optimization problem in such existence condition the vertex system of reduced order model can be obtained which also provides an h gain for the error system between the original system and the reduced order model a numerical example is given to show the effectiveness and the potential of the proposed techniques

a geometrical approach of quasiperiodic tilings tilings provide generalized frames of coordinates and as such they are used in different areas of physics the aim of the present paper is to present a unified and systematic description of a class of tilings which have appeared in contexts as disconnected as crystallography and dynamical systems the tilings of this class show periodic or quasiperiodic ordering and the tiles are related to the unit cube through affine transformations we present a section procedure generating canonical quasiperiodic tilings and we prove that true tilings are indeed obtained moreover the procedure provides a direct and simple characterization of quasiperiodicity which is suitable for tilings but which does not refer to fourier transform

on diffraction by aperiodic structures this paper gives a rigorous treatment of some aspects of diffraction by aperiodic structures such as quasicrystals it analyses diffraction in the limit of the infinite system through an appropriately defined autocorrelation the main results are a justification of the standard way of calculating the diffraction spectrum of tilings obtained by the projection method and a proof of a variation on a conjecture by bombieri and taylor

model reduction of delay systems using pade approximants this paper describes the rational approximation of a certain class of delay systems in the frequency domain using pad approximants of exp st three classes of approximants characterized by their relative degrees are considered easily computable a priori l and l l2error bounds are provided

l 1 impulse response error bound for balanced truncation this paper presents an upper bound in l1 for the impulse response error between a system and its balanced truncation it is an a priori bound and can be computed easily numerical examples are used to illustrate its applications and to compare with other available error bounds

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

design of linear phase iir filters via impulse response gramians a new method for the design of a linear phase infinite impulse response iir filter is presented it involves designing a finite impulse response fir filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order iir filter using model reduction based on impulse response gramians the general outline of the method and a brief overview of the existing linear phase fir filter design and model reduction techniques are presented the impulse response gramian and the model reduction algorithm used are presented the method is illustrated by design examples and is compared with other methods for the design of linear phase iir filters using equalizers

least squares approximation of fir by iir digital filters an algorithm is presented for the least squares approximation of fir filters by iir filters the algorithm is an iterative procedure where each iteration requires the solution of an overdetermined set of linear equations and some digital filtering operations all calculations are performed with the numerator and denominator coefficients of the transfer functions a conversion to state space descriptions is not necessary examples show that the approximation error is as small as that of the iir filters obtained with balanced model reduction moreover the effects of numerical errors are negligible thus our algorithm is applicable even in cases where the fir filter length is large

local rules for quasiperiodic tilings of quadratic 2 planes in r 4 we prove that quasiperiodic tilings of the plane appearing in the strip pro jection method always admit local rules when the linear embedding of i z in 4 has quadratic coefficients these local rules are constructed and studied the connection between novikov quasicrystallographic groups and the quasiperiodic tilings of eu clidean space is explained all the point groups in novikov s sense compatible with these local rules are enlisted the two dimensional quasicrystals with infinite fold rotational symmetry are constructed and studied

a novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure feedback form abstract in this paper a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure feedback systems different from the existing results that are based on traditional back stepping schemes as well as approximation technique of fuzzy logic systems flss for stochastic nonlinear systems this new approach assumes that the norm of optimal approximation parameter vector of flss is bounded by unknown parameter at each design step of this new approach fewer bounded adaptive parameters need to be adjusted thus this new approach can alleviate the online computation burden and improve the robust control performance meanwhile combining lyapunov theorem analysis it is proven that all the signals in the closed loop system are uniformly ultimately bounded uub and the tracking error can converge to a small neighborhood of zero the good performance of this approach is well demonstrated in a simulation example

equivalence of the generalised grid and projection methods for the construction of quasiperiodic tilings the two main techniques for the generation of quasiperiodic tilings de bruijn s grid method 1981 and the projection formalism are generalised a very broad class of quasiperiodic tilings is obtained in this way the two generalised methods are shown to be equivalent the standard calculation of fourier spectra is extended to the whole general class of tilings various applications are discussed

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

min max approximation of transfer functions with application to filter design this paper investigates the problem of frequency specific fs model approximation of transfer functions using a min max approach the objective is to find an approximation model for a transfer function such that the maximum error gain over a specific frequency range is minimized first a linear matrix inequality condition characterizing the fs gain of a transfer function is derived by using the generalized kalman yakubovich popov lemma and then a simple iterative approach is proposed to optimize the approximation model numerical experiments show that the proposed approach can produce better approximation models over a specific frequency range than some existing approaches moreover it is indicated how to apply the proposed approximation approach to the design problem of infinite impulsive response digital filters and design examples clearly illustrate that the proposed design flow can generate filters comparable with the latest design method

tracking control for non gaussian stochastic distribution sampled data fuzzy systems abstract this paper studies the tracking control problem for the non gaussian stochastic distribution sampled data fuzzy systems first by constructing an augmented system an asynchronous proportional integral pi controller is designed such that the probability density functions pdfs of the system output can track the target one second by introducing two sets the extension reachable set and the ellipsoid set the state trajectories of the augmented system with persistent reference input signal can be restricted in a given local region namely the state constrained problem can be addressed furthermore in some existing asynchronous controller strategies it is required that the derivative of the membership function of the system not explicitly depends on the system input however in this paper by restricting the state into a specified region a new asynchronous scheme is proposed so as to the above mentioned requirement is removed finally an example is given to demonstrate the efficiency of the presented method

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

multiplicative approximation of transfer functions with frequency weighting abstract an algorithm for transfer function order reduction is presented which generalizes the balanced stochastic truncation algorithm to allow for input weighting an example illustrates use of the algorithm to secure smaller db error in selected frequency bands through the introduction of the weighting

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

decentralized adaptive output feedback controller design for stochastic nonlinear interconnected systems in this paper the controller design for a class of stochastic interconnected systems with both parametric uncertainties and unknown nonlinear interactions is presented the diffusion terms considered are dependent on the outputs of local subsystems and allowed to be unbounded first by employing decentralized state observers totally decentralized adaptive tracking controllers with suitable parameter adaptive laws are designed to ensure the boundedness in probability of all the signals in the closed loop system it is shown that the tracking errors converge to small residual sets around the origin then for systems with relaxed diffusion vector fields a decentralized adaptive stabilizing scheme is proposed to ensure the boundedness in probability of all signals in the closed loop system

local rules for quasicrystals the relationship of local ordering and long range order is studied for quasicrystalline tilings of plane and space two versions of the concept of local rules are introduced strong and weak necessary conditions of the existence of strong local rules are found they are mainly reduced to the constraints for irrational numbers related to incommensurabilities of the quasicrystals for planar quasicrystals the quadratic irrationalities a b sqrt d left a b in mathbb q d in mathbb z right play an important role for three dimensional quasicrystals not only quadratic but also cubic irrationalities a b 3 sqrt d c 3 sqrt d 2 left a b c in mathbb q d in mathbb z right are allowed the existence of weak local rules is established for almost all two dimensional quasicrystals based on quadratic irrationalities and for the three dimensional quasicrystal having icosahedral symmetry