a cumulant based algorithm for the identification of input output quadratic systems the identification of a special class of polynomial models is pursued in this paper in particular a parameter estimation algorithm is developed for the identification of an input output quadratic model excited by a zero mean white gaussian input and with the output corrupted by additive measurement noise input output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms the output error method and a combination of the instrumental variables and the output error approach the proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator

a note on some recent methods for solving nonlinear equations abstract in this note we present some comments on the recent results concerning iterative methods for solving nonlinear equations in the first part we compare a new method n ujevic a method for solving nonlinear equations appl math comput 174 2006 1416 1426 with the newton and ostrowski method including an extensive analysis of numerical results together with the choice of initial approximations and the computational efficiency of the considered methods in the second part we give a list of recently derived root finding methods and we study the question of priority namely we find out that all reviewed methods were already derived at the beginning of the 60s of the last century one of them dates from the 18th century some remarks on the comparison analysis and the application of iteration methods are included

nonlinear system identification using gaussian inputs the paper is concerned with the identification of nonlinear systems represented by volterra expansions and driven by stationary zero mean gaussian inputs with arbitrary spectra that are not necessarily white procedures for the computation of the volterra kernels both in the time as well as in the frequency domain are developed based on cross cumulant information the derived kernels are optimal in the mean squared error sense for noncausal systems order recursive procedures based on minimum mean squared error reduction are derived more general input output representations that result when the volterra kernels are expanded in a given orthogonal base are also considered

on new exponential quadratically convergent iterative formulae a class of exponential iterative formulae having quadratic convergence is discussed in this paper the theoretical analysis and numerical experiments show that new exponential iterative formulae are effective and comparable to well known method of newton

structural controllability of switched linear systems this paper studies the structural controllability of a class of uncertain switched linear systems where the parameters of subsystems state matrices are either unknown or zero the structural controllability is a generalization of the traditional controllability concept for dynamical systems and purely based on the interconnection relation between the state variables and inputs through non zero elements in the state matrices in order to illustrate such a relationship two kinds of graphic representations of switched linear systems are proposed based on which graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented finally the paper concludes with discussions on the results and future work

construction of third order modifications of newton s method abstract in this paper an approach for constructing third order modifications of newton s method using second order iteration formulas is presented several numerical examples are given to compare some of the newly obtained methods with the other third order methods

reachability realization and stabilizability of switched linear discrete time systems abstract in this paper the reachability realization of a switched linear discrete time system which is a collection of linear time invariant discrete time systems along with some maps for switching among them is addressed the main contribution of this paper is to prove that for a switched linear discrete time system there exists a basic switching sequence such that the reachable controllable state set of this basic switching sequence is equal to the reachable controllable state set of the system hence the reachability controllability can be realized by using only one switching sequence we also discuss the stabilizability of switched systems and obtain a sufficient condition for stabilizability two numeric examples are given to illustrate the results

on reachability and stabilization of switched linear systems reachability and stabilization issues for switched linear control systems are addressed a necessary and a sufficient condition are presented for reachability under mild assumptions we prove that the switched linear control systems are stabilizable in addition we show that an element driven switching stabilization strategy can be explicitly constructed

a note on some higher order modifications of newton s method for solving nonlinear equations abstract in yoonmee ham changbum chun sang gu lee some higher order modifications of newtons method for solving nonlinear equations j comput appl math in press doi 10 1016 j cam 2007 11 018 a method to construct some higher order modifications of newton s method has been presented in this paper we show that the main result given by the authors is not accurate for p 1 and p 2 some counterexamples are given to verify our analysis

a one parameter family of quadratically convergent iteration formulae a new one parameter family of iteration methods for solving nonlinear equations is presented the convergence analysis shows that their order of convergence is two numerical examples are given to illustrate the efficiency and performance of the proposed methods

extended generalized total least squares method for the identification of bilinear systems the extended generalized total least squares e gtls method that consider the special structure of the data matrix is proposed as one of the bilinear system parameters considering that the input is noise free and that bilinear system equation is linear with respect to the output we extend the gtls problem the extended gtls problem is reduced to an unconstrained minimization problem and is then solved by the newton raphson method we compare the gtls method and the extended gtls method as far as the accuracy of the estimated system parameters is concerned

on controllability of switched linear systems in this paper the controllability of a switched linear system which is a collection of linear time invariant systems along with some maps for switching among them is addressed first a controllable state set is defined as a basic tool to discuss the controllability condition next it is proved that the controllability of a multi input system is equivalent to that of a single input system finally a sufficient and necessary condition for controllability of third order systems is presented according to the proof of this criterion we state a conjecture on the controllability condition of n dimensional systems a numeric example is given to illustrate the result

identification of input output bilinear systems using cumulants this paper is concerned with the identification of a discrete input output bilinear system driven by an independent identically distributed i i d stochastic input and corrupted by measurement noise a novel algorithmic procedure for the direct computation of the unknown model parameters is developed based on crosscumulant information up to third order simulations and comparisons with a least squares type identification method are provided

on a class of quadratic convergence iteration formulae without derivatives a class of iterative formulae without derivatives are proposed in this paper these methods are shown to be quadratic convergence some numerical tests are given

technical communique necessary and sufficient condition for the controllability of switching linear hybrid systems controllability of switching linear hybrid systems by means of algebraic conditions was discussed by yang automatica 38 2002 1221 this paper shows that algebraic conditions complemented with an assumption on the switching function provides not only necessary but also sufficient condition for the problem the relation of these algebraic conditions with an invariant subspace algorithm is also presented

on the construction of iterative methods with at least cubic convergence using the iteration formulas of order two for solving nonlinear equations we present a basic tool for deriving new higher order iterative methods that do not require the computation of the second order or higher order derivatives the presented convergence analysis shows that the order of convergence of the obtained iterative methods are three or higher the comparison with other methods is given

third order and fourth order iterative methods for finding multiple and distinct zeros of non linear equations in this paper we point out and analyse six two step iterative methods for finding multiple as well as distinct zeros of non linear equations we prove that the methods for multiple zeros have third order convergence where as the methods for distinct zeros have fourth order convergence the methods calculate the multiple as well as distinct zeros with high accuracy the numerical tests show their better performance in case of algebraic as well as non algebraic equations

a note on some new iterative methods with third order convergence abstract in j h chen some new iterative methods with three order convergence appl math comput 181 2006 1519 1522 some new iterative methods were proposed and proved to be third order convergence in this paper some mistakes are pointed out in the derivation of these new methods an analysis is given to show that these new iterative methods converge only linearly

certain improvements of newton s method with fourth order convergence in this paper we present two new schemes one is third order and the other is fourth order these are improvements of second order methods for solving nonlinear equations and are based on the method of undetermined coefficients we show that the fourth order method is more efficient than the fifth order method due to kou et al j kou y li x wang some modifications of newton s method with fifth order covergence j comput appl math 209 2007 146 152 numerical examples are given to support that the methods thus obtained can compete with other iterative methods

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

ball convergence comparison between three iterative methods in banach space under hypothese only on the first derivative we present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a banach space setting the convergence ball and error estimates are given for these methods under hypotheses only on the first frechet derivative in contrast to earlier studies such as adomian 1994 1 babajee et al 2008 13 cordero and torregrosa 2007 17 cordero et al 18 darvishi and barati 2007 19 using hypotheses reaching up to the fourth frechet derivative although only the first derivative appears in these methods this way we expand the applicability of these methods numerical examples are also presented in this study

maximum likelihood parameter estimation of bilinear systems this paper addresses the problem of estimating the parameters in a multivariable bilinear model on the basis of observed input output data the main contribution is to develop analyze and empirically study new techniques for computing a maximum likelihood based solution in particular the emphasis here is on developing practical methods that are illustrated to be numerically reliable robust to choice of initialization point and numerically efficient in terms of how computation and memory requirements scale relative to problem size this results in new methods that can be reliably deployed on systems of nontrivial state input and output dimension underlying these developments is a new approach in this context of employing the expectation maximization method as a means for robust and gradient free computation of the maximum likelihood solution

adaptive stabilization of bilinear systems for a class of deterministic and stochastic bilinear systems modified self tuning regulators are given by using recursive least squares and modified recursive least squares respectively the closed loop systems are shown globally stable and asymptotically optimal in some sense without any restriction on location of poles or zeros of nominal linear part of the open loop system considered simulations show that the methods used here work very well

a one parameter family of second order iteration methods a new one parameter family of iteration methods for finding simple roots of nonlinear equations is developed error analysis providing the second order convergence is given numerical experience shows that the method is comparable to the well known newton s method

a fourth order iterative method for solving nonlinear equations the present paper illustrates an iterative numerical method to solve nonlinear equations of the form f x 0 especially those containing the partial and non partial involvement of transcendental terms comparative analysis shows that the present method is faster than newton raphson method hybrid iteration method new hybrid iteration method and others cost is also found to be minimum than these methods the beauty in our method can be seen because of the optimization in important effecting factors i e lesser number of iteration steps lesser number of functional evaluations and lesser value of absolute error in final as well as in individual step as compared to the other methods this work also demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative

a sixth order method for nonlinear equations abstract in this paper a sixth order method is developed by extending a third order method of weerakoon and fernando s weerakoon t g i fernando a variant of newton s method with accelerated third order convergence appl math lett 13 2000 87 93 for finding the real roots of nonlinear equations in r starting with a suitably chosen x 0 the method generates a sequence of iterates converging to the root the convergence analysis is provided to establish its sixth order of convergence in terms of computational cost it requires evaluations of only two functions and two first derivatives per iteration this implies that efficiency index of our method is 1 565 our method is comparable with the methods of neta b neta a sixth order family of methods for nonlinear equations intern j computer math 7 1979 157 161 and that of kou and li jisheng kou yitian li an improvement of jarratt method appl math comput 189 2007 1816 1821 it does not require the evaluation of the second order derivative of the given function as required in the family of chebyshev halley type methods jisheng kou xiuhua wang sixth order variants of chebyshev halley methods for solving non linear equations appl math comput 190 2007 1839 1843 jisheng kou on chebyshev halley methods with sixth order convergence for solving non linear equations appl math comput 190 2007 126 131 the efficacy of the method is tested on a number of numerical examples it is observed that our method takes less number of iterations than newton s method and the method of weerakoon and fernando on comparison with the other sixth order methods it behaves either similarly or better for the examples considered

some third order families of iterative methods for solving nonlinear equations abstract in this paper we present a convenient third order iteration formula improving newton s method for solving nonlinear equations with any two iteration functions of order two the formula provides one parameter third order family of methods each family member is free from second derivatives and per iteration it requires three evaluations of the given function and its derivative several numerical examples are given to illustrate the efficiency and performance of some of the presented methods

three step iterative methods for nonlinear equations in this paper we suggest and analyze a new three step iterative method for solving nonlinear equations we show that this new iterative method has third order convergence several numerical examples are given to illustrate the efficiency and performance of the new method

identification of structurally constrained second order volterra models continuing advances in industrial control hardware and software have increased interest in the identification of nonlinear dynamic models from chemical process data two practically important issues are those of nonlinear model structure selection and input sequence design for adequate model identification while the general nonlinear model identification problem is intractably complex we may obtain useful insights into both of these issues by restricting our attention to special cases building incrementally on our linear intuition we consider the special case of second order volterra models focusing on the effects of structural restrictions and non gaussian input sequences on the model identification problem the results presented build on the work of powers and his co workers who considered the unconstrained gaussian problem certain constrained special cases e g the hammerstein model and identification using non i i d input sequences besides extending these results to a wider class of model structure constraints and input sequences the results presented yield some useful insights into the issue of input sequence design

third order derivative free sph iterative method for solving nonlinear systems the majority of iterative methods to find roots of a function requires the evaluation of derivatives of this function in this paper based on the basic principle of the sph method s kernel approximation a kernel approximation was constructed to compute first and second order derivatives through taylor series expansion derivatives in our proposed method were replaced in a newton like iterative method to obtain a derivative free sph iterative method for solving nonlinear systems to illustrate that the new method has the same order of convergence as the considered iterative method some numerical examples are presented

reachability of linear switched systems differential geometric approach the paper investigates the structure of the reachable set of linear switched systems the structure of the reachable set is determined using techniques from classical nonlinear systems theory namely the theory of orbits developed by h sussman and the realization theory for nonlinear systems developed by b jakubczyk

reachability and controllability of switched linear discrete time systems this paper investigates the reachability and controllability issues for switched linear discrete time systems geometric characterization of controllability is presented for reversible systems the controllable sets and the reachable sets are identified in wonham s geometric approach and verifiable conditions for reachability and controllability are also presented

new high order convergence iteration methods without employing derivatives for solving nonlinear equations abstract a family of new iteration methods without employing derivatives is proposed in this paper we have proved that these new methods are quadratic convergence their efficiency is demonstrated by numerical experiments the numerical experiments show that our algorithms are comparable to well known methods of newton and steffensen furthermore combining the new method with bisection method we construct another new high order iteration method with nice asymptotic convergence properties of the diameters b n a n

a stability condition for certain bilinear systems the authors derive a simple sufficient condition for the output of a discrete time time invariant bilinear system to be bounded whenever the input signal to the system is bounded by a finite constant

new modified regula falsi method for nonlinear equations abstract this paper employs two new iterative methods accelerating convergence after using the classical regula falsi methods such that both the sequence of diameters b n a n n 1 and the sequence of iteration x n x n 1 produced by the new methods quadratically converge to zero the numerical experiments show that new methods are effective and comparable to some well known methods

on the controllability of switching linear systems this note presents a necessary and sufficient condition for small time controllability of a linear switching system that is a collection of linear time invariant control systems where a trajectory is any concatenation of trajectories of the individual systems this result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone

some new iterative methods with three order convergence some new iterative formulae having three order convergence are discussed in this paper the theoretical analysis and numerical experiments show that new iterative formulae are effective and comparable to well known method of newton and stefensen method

fourth order convergent iterative method for nonlinear equation in this paper we suggest and analyze a new iterative method for finding approximate solution of the nonlinear equation f x 0 it is shown that proposed method has fourth order convergence several numerical examples are given to illustrate that the method developed in this paper give better results than the other methods including newton method

blind identification of bilinear systems this paper is concerned with the blind identification of a class of bilinear systems excited by non gaussian higher order white noise the matrix of coefficients of mixed input output terms of the bilinear system model is assumed to be triangular in this work under the additional assumption that the system output is corrupted by gaussian measurement noise we derive an exact parameter estimation procedure based on the output cumulants of orders up to four results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

brief an algebraic approach towards the controllability of controlled switching linear hybrid systems based on the hybrid controllability concept ieee automat control 43 4 1998 491 the controllability problem for a class of hybrid control systems referred to as controlled switching linear hybrid systems is discussed one sufficient condition and one necessary condition are derived by employing algebraic manipulations of related system matrices the computational test of these conditions and some examples are also discussed

on some third order iterative methods for solving nonlinear equations using the iteration formulas of second order mamta v kanwar v k kukreja sukhjit singh on a class of quadratically convergent iteration formulae appl math comput 2004 in press for solving single variable nonlinear equations two classes of third order multipoint methods without using second derivative are derived the main advantage of these classes is that they do not fail if the derivative of the function is either zero or very small in the vicinity of the required root further a new family of secant like method with guaranteed super linear convergence is obtained by discrete modifications and their comparison with respect to the existing classical methods is given

second order volterra system identification second order volterra system identification is discussed crosscumulant information is converted into a fredholm integral equation special emphasis is focused on inputs obtained at the output of a linear filter driven by higher order white noise

realization theory for linear switched systems formal power series approach the paper deals with the realization theory of linear switched systems necessary and sufficient conditions are formulated for a family of input output maps to be realizable by linear switched systems characterization of minimal realizations is presented the paper treats two types of linear switched systems the first one is when all switching sequences are allowed the second one is when only a subset of switching sequences is admissible but within this restricted set the switching times are arbitrary the paper uses the theory of formal power series to derive the results on realization theory

some higher order modifications of newton s method for solving nonlinear equations in this paper we consider constructing some higher order modifications of newton s method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units this construction can be applied to any iteration formula and per iteration the resulting methods add only one additional function evaluation to increase the order some illustrative examples are provided and several numerical results are given to show the performance of the presented methods

accessibility of switched linear systems this note considers the controllability of switched linear systems the structure of accessibility lie algebra is revealed some accessibility properties are proved certain necessary and sufficient conditions for local or global weak or normal controllability of a large class of switched linear systems are obtained

on a class of quadratically convergent iteration formulae in this paper a new class of iterative formulae having quadratic convergence is presented furthermore these algorithms are comparable to the well known method of newton and the computed results support this theory

brief paper design of switching sequences for controllability realization of switched linear systems in this paper we study the problem of designing switching sequences for controllability of switched linear systems each controllable state set of designed switching sequences coincides with the controllable subspace both aperiodic and periodic switching sequences are considered for the aperiodic case a new approach is proposed to construct switching sequences and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d d d 1 1 here d is the dimension of the controllable subspace d email protected i 1 m where a i b i are subsystems for the periodic case we show that the controllable subspace can be realized within d switching periods

controllability and stabilizability of switched linear systems in this paper we study the conjecture made in ieee trans automat control 47 8 2002 1401 concerning the existence of basic switching sequence for switched systems and give it an affirmative answer and a construction method this paper proves that for switched linear system there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system hence the controllability can be realized by using only one switching sequence then the result is extended to the systems with time delay in controls furthermore we define the stabilizability of switched linear systems and based on certain transformation of state coordinate we give a necessary and sufficient condition for the stabilizability two examples are presented to illustrate the obtained results

efficient algorithms for volterra system identification in this paper nonlinear filtering and identification based on finite support volterra models are considered the volterra kernels are estimated via input output statistics or directly in terms of input output data it is shown that the normal equations for a finite support volterra system excited by zero mean gaussian input have a unique solution if and only if the power spectral process of the input signal is nonzero at least at m distinct frequencies where m is the memory of the system a multichannel embedding approach is introduced a set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format efficient algorithms for the estimation of the volterra parameters are derived for batch as well as for adaptive processing an efficient order recursive method is presented for the determination of the volterra model structure the proposed methods are illustrated by simulations

a geometric construction of iterative functions of order three to solve nonlinear equations in this paper we consider a geometric construction of iteration functions of order three to develop cubically convergent iterative methods for solving nonlinear equations this construction can be applied to any iteration function of order two to develop an iteration function of order three some examples are given of deriving several third order iteration methods and several numerical results follow to illustrate the performance of the derived methods

a class of exponential quadratically convergent iterative formulae for unconstrained optimization abstract for solving nonlinear univariate and unconstrained optimization problems newton method is an important and basic method which converges quadratically this paper presents a class of exponential iterative formulae convergence analyses show that the proposed methods converge quadratically the efficiencies of the methods are analyzed in terms of the most popular and widely used criterion in comparison with the classical newton method using five test functions numerical results indicate that one of the new exponential iterative formulae is effective and comparable to well known newton s method

some quadrature based three step iterative methods for non linear equations in this paper we present three step quadrature based iterative methods for solving non linear equations the convergence analysis of the methods is discussed it is established that the new methods have convergence order six seven and eight respectively numerical tests show that the new methods are comparable with the well known existing methods and in many cases give better results our results can be considered as an improvement and refinement of the previously known results in the literature

on iterative methods for nonlinear equations several iterative methods have been suggested and analyzed for solving nonlinear equation f x 0 all these methods can be classified as one step and two step methods in this paper we have suggested and analyzed several two step methods for solving nonlinear equations we have also shown that these two step methods are quadratically convergent several numerical examples are given to illustrate this comparison our results can be viewed as important refinement and improvement of the previously known results

a novel cubically convergent iterative method for computing complex roots of nonlinear equations abstract a fast and simple iterative method with cubic convergent is proposed for the determination of the real and complex roots of any function f x 0 the idea is based upon passing a defined function g x tangent to f x at an arbitrary starting point choosing g x in the form of x k or k x where k is obtained for the best correlation with the function f x gives an added freedom which in contrast to all existing methods accelerates the convergence also this new method can find complex roots just by a real initial guess this is in contrast to many other methods like the famous newton method that needs complex initial guesses for finding complex roots the proposed method is compared to some new and famous methods like newton method and a modern solver that is fsolve command in matlab the results show the effectiveness and robustness of this new method as compared to other methods

technical communique a new perspective on criteria and algorithms for reachability of discrete time switched linear systems the paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete time systems direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability reachability algorithm and kalman type algebraic rank criteria also the existing geometric criteria is simplified and new algebraic conditions on controllability and reachability are given