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

structured squaring down and zero assignment the problem of zero assignment by squaring down is considered for a system of p inputs n outputs and n states m p where not all outputs are free variables for design we consider the case where a k subset of outputs is preserved in the new output set and the rest are recombined to produce a total new set of p outputs new invariants for the problem are introduced which include a new class of fixed zeros and the methodology of the global linearization developed originally for the output feedback pole assignment problem is applied to this restricted form of the squaring down problem it is shown that the problem can be solved generically if p k m p where k k p is the number of fixed outputs and is a system and compensation scheme invariant which is defined as the restricted forney degree

pole placement by static output feedback for generic linear systems we consider linear systems with m inputs p outputs and mcmillan degree n such that n mp if both m and p are even we show that there is a nonempty open in the usual topology subset u of such systems where the real pole placement map is not surjective it follows that for each system in u there exists an open set of pole configurations symmetric with respect to the real line which cannot be assigned by any real static output feedback

approximation algorithms for the shortest common superstring problem abstract the object of the shortest common superstring problem scs is to find the shortest possible string that contains every string in a given set as substrings as the problem is np complete approximation algorithms are of interest the value of an aproximate solution to scs is normally taken to be its length and we seek algorithms that make the length as small as possible a different measure is given by the sum of the overlaps between consecutive strings in a candidate solution when considering this measure the object is to find solutions that make it as large as possible these two measures offer different ways of viewing the problem while the two viewpoints are equivalent with respect to optimal solutions they differ with respect to approximate solutions we describe several approximation algorithms that produce solutions that are always within a factor of two of optimum with respect to the overlap measure we also describe an efficient implementation of one of these using mccreight s compact suffix tree construction algorithm the worstcase running time is o m log n for small alphabets where m is the sum of the lengths of all the strings in the set and n is the number of strings for large alphabets the algorithm can be implemented in o m log m time by using sleator and tarjan s lexicographic splay tree data structure

robust pid controller tuning based on the constrained particle swarm optimization this paper proposes a novel tuning strategy for robust proportional integral derivative pid controllers based on the augmented lagrangian particle swarm optimization alpso first the problem of pid controller tuning satisfying multiple h performance criteria is considered which is known to suffer from computational intractability and conservatism when any existing method is adopted in order to give some remedy to such a design problem without using any complicated manipulations the alpso based robust gain tuning scheme for pid controllers is introduced it does not need any conservative assumption unlike the conventional methods and often enables us to find the desired pid gains just by solving the constrained optimization problem in a straightforward way however it is difficult to guarantee its effectiveness in a theoretical way because pso is essentially a stochastic approach therefore it is evaluated by several simulation examples which demonstrate that the proposed approach works well to obtain pid controller parameters satisfying the multiple h performance criteria

optimization of static output feedback using substitutive lmi formulation this note proposes a new design tool for optimizing static output feedback using a linear matrix inequality lmi formula called substitutive lmi a matrix inequality derived from static output feedback is not usually linear adding a positive definite term including auxiliary variables the matrix inequality is transformed into an lmi with respect to the positive definite matrix and the static output feedback gain an iterative calculation algorithm is given to solve the substitutive lmi in this note designs of the static output feedback gain are shown in the frame of h sub spl infin and h sub 2 syntheses a numerical example is shown to demonstrate the effectiveness of the proposed technique

some remarks on real and complex output feedback we provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers we exhibit a nontrivial real linear system which is not controllable by real static output feedback and discuss a conjecture from algebraic geometry concerning the existence of real linear systems for which all static feedback laws are real

quadratically parameterized root locus analysis classical affine root locus applies to controllers that are linear in a parameter k and yield affinely parameterized closed loop denominator polynomials this paper presents root locus rules for controllers that are rational in k and yield quadratically parameterized closed loop denominator polynomials we show that the quadratic root locus has several advantages relative to the classical affine root locus specifically the quadratic root locus is high parameter stabilizing for minimum phase systems that are relative degree 1 2 or 3 moreover the quadratic root locus admits a wider variety of asymptote angles which provides more controller design flexibility the quadratic root locus is illustrated on several examples that are difficult to handle using affine root locus such as high parameter stabilization of the triple integrator

some results on the genericity of the pole placement problem abstract in this note the pole placement problem for a linear mimo systems with p outputs and m inputs is studied from the algebraic point of view a formulation is proposed that allows to analyze both theoretical and numerical aspects of the case min m p 2 with more sharpness moreover here it is shown that arbitrary pole placement by static output feedback of unitary rank is generically not possible even if m p n holds true

stabilization of discrete time linear systems by static output feedback this note proposes a systematic approach for the static output feedback control design for discrete time linear systems it is shown that if the open loop system satisfies some particular structural conditions a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the stronger relies on a minimum phase argument square and nonsquare systems are considered

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 feedback and generic stabilizability we consider questions of pole placement and stabilization for generic linear systems with prescribed state input and output dimensions where the controller must be implemented by linear memoryless output feedback we present a criterion in terms of a special pole placement property for generic stabilizability and apply this to describe constraints on the dimensions which are consistent with generic stabilizability we also discuss the rationality and solvability by radicals of stabilizing or pole positioning gains and we describe how decision algebra can theoretically handle existence questions for generic systems

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

the mcmillan and newton polygons of a feedback system and the construction of root loci abstract the local behaviour of root loci around zeros and poles is investigated this is done by relating the newton diagrams which arise in the local analysis to the mcmillan structure of the open loop system by means of what we shall call the mcmillan polygon this geometric construct serves to clarify the precise relationship between the mcmillan structure the principal structure and the branching patterns of the root loci in addition several rules are obtained which are useful in the construction of the root loci of multivariable control systems

grassmann invariants almost zeros and the determinantal zero pole assignment problems of linear multivariable systems the strucxpects of the rationxr spaces x c x fwhere x c is the columxof the transfer function matrix g s and x f is the space associated with right matrix fracxcriptions of g s are investigated for x f gcanonixqb s grassmgesentax g x c and g x f arxd and are shown xmplete basis free invariants for x c and x f respectively the almost zeros az and almost decoupling zeros adz of g s gdefinex local minima of a normgn defix g x c and g x f respectively the computation and certain aspects of the distribution in the complex plane of azs and adzs are examined the role of azs and adzs in the determinantal zero and pole assignment problems respectively is examined next two important families of systems are defined the strongly zero non assignable szna and the strongly pole non assignable spna systems for szna and spna systems minimal radius discs dem e z r em e z and dem f zb centred at an az and adz respectively are defined it is shown that dem e r em e z contains at least one zer

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

on linear solutions of the output feedback pole assignment problem a new linear method for solving the output feedback pole assignment problem of linear systems is introduced and new sufficient conditions are obtained

chaos driven evolutionary algorithms for the task of pid control chaos driven differential evolution algorithm and self organizing migrating algorithm are presented in this paper for the task of pid proportional integral derivative controller optimization the dissipative chaotic lozi map is embedded as a number generator inside de and soma in order to avoid local optima stagnation and embed a superior search strategy three unique pid controller problems are presented and successfully resolved using these new approaches the obtained results compare favorably with published results

generic eigenvalue assignment by memoryless real output feedback by extensive use of methods from algebraic geometry x wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states m inputs and p outputs if n mp here we show the same result using no more of algebraic geometry than the definition of genericity

computing dynamic output feedback laws the pole placement problem asks to find laws to feed the output of a plant governed by a linear system of differential equations back to the input of the plant so that the resulting closed loop system has a desired set of eigenvalues converting this problem into a question of enumerative geometry efficient numerical homotopy algorithms to solve this problem for general multiple input multiple output systems have been proposed recently despite the wider application range of dynamic feedback laws the realization of the output of the numerical homotopies as a machine to control the plant in the time domain has not been addressed before in this note we present symbolic numeric algorithms to turn the solution to the question of enumerative geometry into a useful control feedback machine we report on numerical experiments with our publicly available software phcpack and illustrate its application on various control problems from the literature

multivariable singularly perturbed feedback systems with time delay multivariable singularly perturbed systems with both small and large time delays in the feedback loop are considered conditions for stability of the full order closed loop system are given in terms of properties of the slow and fast subsystems

approximating shortest superstrings with constraints various versions of the shortest common superstring problem play important roles in data compression and dna sequencing only recently the open problem of how to approximate a shortest superstring given a set of strings was solved in 1 9 1 shows that several greedy algorithms produce a supeistring of length o n where n is the optimal length however a major problem remains open can we still linearly approximate a superstring in polynomial time when the superstring is required to be consistent with some given negative strings i e it must not contain any negative string the best previous algorithm group merge given in 6 9 produces a consistent superstring of length n log n the negative strings make the problem much more difficult and as we will show a greedy style algorithm cannot achieve linear approximation for this problem

periodically varying compensation of time invariant systems linear time invariant discrete time scalar systems under periodically varying output feedback and the associated problems of stabilization and arbitrary eigenvalue assignment are investigated the general form of the characteristic polynomial of the closed loop periodically varying system is obtained and some detailed results are provided for the second order case interesting research questions are pointed out

firefly algorithm approach based on chaotic tinkerbell map applied to multivariable pid controller tuning nowadays a variety of controllers used in process industries are still of the proportional integral derivative pid types pid controllers have the advantage of simple structure good stability and high reliability a relevant issue for pid controllers design is the accurate and efficient tuning of parameters in this context several approaches have been reported in the literature for tuning the parameters of pid controllers using evolutionary algorithms mainly for single input single output systems the systematic design of multi loop or decentralized pid control for multivariable processes to meet certain objectives simultaneously is still a challenging task this paper proposes a new chaotic firefly algorithm approach based on tinkerbell map cfa to tune multi loop pid multivariable controllers the firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies to validate the performance of the proposed pid control design a multi loop multivariable pid structure for a binary distillation column plant wood and berry column model and an industrial scale polymerization reactor are taken simulation results indicate that a suitable set of pid parameters can be calculated by the proposed cfa besides some comparison results of a genetic algorithm a particle swarm optimization approach traditional firefly algorithm modified firefly algorithm and the proposed cfa to tune multi loop pid controllers are presented and discussed

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

output feedback pole assignment for transfer functions with symmetries this paper studies the problem of pole assignment for symmetric and hamiltonian transfer functions a necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given moreover in the case where the mcmillan degree coincides with the number of parameters appearing in the symmetric feedback transformations we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains the proof uses intersection theory in projective space as well as a formula for the degree of the complex lagrangian grassmann manifold

brief paper multivariable pid control with set point weighting via bmi optimisation the paper focuses on the design of multivariable pid controllers with set point weighting the advantage of this pid structure is that the responses of the system to disturbances and to changes in the set point can be adjusted separately the proposed design methods rely on the transformation of the tuning of the controller gains into a static output feedback sof problem hence multivariable pid controllers can be designed by solving an optimisation problem with bilinear matrix inequalities bmis the paper addresses the design of both time invariant and gain scheduled robust controllers all of the tuning methods discussed through the paper are based on a pid structure with filtered derivative term thus guaranteeing the well posedness of the closed loop system

shortest consistent superstrings computable in polynomial time abstract the shortest consistent superstring problem is given a set of positive strings and a set of negative strings finding a shortest string including every positive string and no negative string as a substring this problem is np hard and arises in dna sequencing by hybridization it is also an extension of the well known shortest common superstring problem which corresponds to the case when the set of negative strings is empty in this paper we show that a shortest consistent superstring can be found in polynomial time if i a longest common nonsuperstring for the set of negative strings exists or ii the number of positive strings is bounded and every symbol of the alphabet appears at the end of some negative string in the case i a longest consistent superstring can also be found in polynomial time

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

a self adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization evolutionary algorithms eas have yielded promising results for solving nonlinear non differentiable and multi modal optimization problems due to its population based nature eas can avoid being trapped in a local optimum and consequently have the ability to find global optimal solutions as a novel evolutionary technique differential evolution de has received increasing attention and wide applications in a variety of fields de algorithm uses an efficient way of self adapting mutation using small populations for function optimization over continuous spaces the potentialities of de are its simple structure easy use convergence property quality of solution and robustness in this paper an effective self adaptive de algorithm based on gaussian probability distribution gamma distribution and chaotic sequence degc for solving continuous global optimization problems is proposed the proposed degc algorithm is tested on several benchmark functions from the usual literature numerical results comparisons with a classical de approach and a self adaptive de approach demonstrate the effectiveness and efficiency of the proposed degc algorithm

a necessary condition for pole assignment by constant output feedback in this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques in particular a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed loop system to any desired positions

static output feedback pole placement via a trust region approach this technical note presents two closely related algorithms for the problem of pole placement via static output feedback the algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm while desired poles must be distinct strategies for dealing with repeated poles are also presented

self organizing genetic algorithm based tuning of pid controllers this paper proposes a self organizing genetic algorithm soga with good global search properties and a high convergence speed first we introduce a new dominant selection operator that enhances the action of the dominant individuals along with a cyclical mutation operator that periodically varies the mutation probability in accordance with evolution generation found in biological evolutionary processes next the soga is constructed using the two operators mentioned above the results of a nonlinear regression analysis demonstrate that the self organizing genetic algorithm is able to avoid premature convergence with a higher convergence speed and also indicate that it possesses self organization properties finally the new algorithm is used to optimize proportional integral derivative pid controller parameters our simulation results indicate that a suitable set of pid parameters can be calculated by the proposed soga

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

a general formula for eigenvalue assignment by static output feedback with application to robust design in this note generalizing an idea of a previous paper we derive a new expression of the characteristic polynomial of a linear system subject to static output feedback from this expression an explicit form of the assignment equations in the unknown elements of the feedback matrix is obtained the equations are completely general and seem much simpler than many others proposed until now in special cases a closed or almost a closed form solution is obtained the assignment equations are then used within an algorithm for global optimization to solve the problem of exactly assigning the eigenvalues of the nominal plant while maximizing the norm of perturbation matrices for which the perturbed eigenvalues remain in specified regions of the complex plane

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

cascade equivalence of linear systems abstract this paper concerns the characterization of a linear system with respect to output feedback as well as to slightly more general transformations called cascade transformations with a transfer function t s we associate a finite tuplee of numbers that is invariant under cascade transformation

eigenvalue assignment by static output feedback on a new solvability condition and the computation of low gain feedback matrices in this article the static output feedback problem for linear time invariant systems is considered for arbitrary assignability of the roots of the characteristic polynomial by static output feedback a new necessary and sufficient condition is derived although the proof is based on simple analysis the known sufficient conditions derived by techniques of algebraic geometry are directly covered furthermore an algorithm for the calculation of feedback matrices assigning a desired set of eigenvalues is proposed this algorithm does not require the desired eigenvalues to be distinct and it explicitly exploits the available degrees of freedom for reducing the feedback gain the presented approach is illustrated on computational examples

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

on pole placement via eigenstructure assignment approach this note comes back to the hard problem of pole placement by static output feedback let a triplet of matrices a b c be given with n state variables m inputs and p ouputs find a matrix k such that the spectrum of a bkc equals a specified set when mp m p a simple noniterative technique based upon the notion of eigenstructure that in most cases assigns m p roots is proposed it therefore enables the designer to assign the whole of the desired spectrum when m p n mp

modeling and model predictive control of a nonlinear hydraulic system this paper deals with modeling and control of a hydraulic three tank system a process of creating a computer model in the matlab simulink environment is described and optimal pid proportional integral derivative and model predictive controllers are proposed the modeling starts with the creation of an initial mathematical model based on a first principles approach then the initial model is enhanced to obtain better correspondence with a real time system and parameters of the modified system are identified from measurements the real time system contains nonlinearities which cannot be neglected and therefore are identified and included in the final mathematical model the resulting model is used for a control design as the real time system has long time constants usage of the simulink model dramatically speeds up the design process optimal pid and model predictive controllers mpc are proposed and compared model predictive controllers for both a linearized model and the nonlinear system are proposed the techniques described are not limited to one particular modeling problem but can be used as an illustrative example for the modeling of many technological processes

a parametric solution to the pole assignment problem using dynamic output feedback a technique is presented for pole placement of linear time invariant systems using dynamic feedback a previously developed method for partial pole assignment using constant feedback is generalized to the dynamic output feedback case subject to a mild assumption on the number of complex conjugate poles to be assigned it is almost always possible to arbitrarily assign all the closed loop system poles using a compensator of order n spl phi max m l using this new method here n m and l are the order of the system and the number of inputs and outputs respectively and spl phi spl delta max m l max m l 2 max m l min m l where x denotes the nearest integer lower than or equal to x i e floor x and x denotes the nearest integer greater than or equal to x i e ceiling x an equivalent result is that using a compensator of order q it is almost always possible to arbitrarily assign min n q max m l 1 q spl phi closed loop system poles only the normal procedures of linear algebra are required to implement the technique note that spl phi spl ges l m 1 and therefore the result is stronger than previous exact pole assignment results since it does not involve iteration or any other numerical techniques it is possible to implement the method symbolically and therefore to obtain general parametric solutions to the pole assignment problem the freedom in this design approach can also often be used to guarantee the internal stability and or robustness of the resulting closed loop system

on static output feedback stabilization of systems with stable generalized zero dynamics in this note we define generalized zero dynamics introduce a generalized zero dynamics algorithm and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback

a sufficient condition for arbitrary eigenvalue assignment in linear descriptor systems by output feedback the problem of eigenvalue assignment in the linear descriptor system e mathdotx ax bu y cx via output feedback is considered it is shown that mp rank e m and p are respectively the numbers of inputs and outputs of the system is a sufficient condition for generic real output feedback eigenvalue assignability the result is the best possible for general m p rank e in general the assignment is achieved not in an exact sense but in arbitrarily small neighborhoods around a given set of eigenvalues

a simplified version of mamdani s fuzzy controller the natural logic controller this paper proposes the natural logic controller nlc that it comes through a very important simplification of the mamdani s fuzzy controller mfc allowing easy design for single input single output siso regulation problems usually fuzzy controllers are built with two classical signals of process the error and its rate of change they use a moderate number of fuzzy subsets and fuzzy rules the main features of the nlc approach are that use the minimal fuzzy partition only two fuzzy subsets per variable and it use the minimal fuzzy rule base only two rules the nonlinear resulting fuzzy controller is the simplest one with an analytically well defined input output mapping and accepting a linear approximation at origin it allows easy extension to more than two signals of process some properties of nonlinear mapping of nlc are analyzed and some results are also presents on testing stability when nlc is used on a linear process a special attention is addressed to the two inputs nlc case where stability can be tested using the circle criterion finally two application examples are discussed in details

identification and estimation of dynamic errors in variables models abstract we consider here the factor analysis approach to the analysis of linear dynamic errors in variables models identification of the most general models and the question of nonuniqueness are discussed we show how these models are generalizations of the total least squares model and how the grassmann manifold provides a natural setting for their analysis under certain assumptions we analyze the problem of maximum likelihood estimation and indicate how this involves maximization of a functional on a grassmann manifold

exact pole assignment with regularity by output feedback in descriptor systems part 2 in this paper the first of two we examine the problem of modal control of linear time invariant multivariable descriptor systems in particular for systems satisfying a certain inequality we will give necessary and sufficient conditions for the existence of an output feedback matrix possibly complex which exactly assigns an arbitrary set of r the number of independent semi state variables of the system distinct complex numbers to a generalized eigenspectrum of the closed loop system while ensuring that the resulting system has a unique smooth solution for each admissible initial condition furthermore it is shown that if the set of proposed poles contains only real elements the assignment can be carried out using real feedback next we present conditions that are necessary and sufficient for pole assignability by real feedback of a self conjugate set of complex numbers provided that the system satisfies a further inequality

output feedback pole placement with dynamic compensators derives a new rank condition which guarantees the arbitrary pole assignability of a given system by dynamic compensators of degree at most q by using this rank condition the authors establish several new sufficiency conditions which ensure the arbitrary pole assignability of a generic system the authors proofs also come with a concrete numerical procedure to construct a particular compensator which assigns a given set of closed loop poles