two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

two new families of sixth order methods for solving non linear equations in this paper we developed two new families of sixth order methods for solving simple roots of non linear equations per iteration these methods require two evaluations of the function and two evaluations of the first order derivatives which implies that the efficiency indexes of our methods are 1 565 these methods have more advantages than newton s method and other methods with the same convergence order as shown in the illustration examples finally using the developing methodology described in this paper two new families of improvements of jarratt method with sixth order convergence are derived in a straightforward manner notice that kou s method in jisheng kou yitian li an improvement of the jarratt method appl math comput 189 2007 1816 1821 and wang s method in xiuhua wang jisheng kou yitian li a variant of jarratt method with sixth order convergence appl math comput 204 2008 14 19 are the special cases of the new improvements

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

a hybrid iterative scheme for mixed equilibrium problems and fixed point problems the purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem mep and the set of common fixed points of finitely many nonexpansive mappings in a real hilbert space first by using the well known kkm technique we derive the existence and uniqueness of solutions of the auxiliary problems for the mep second by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings furthermore we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of mep and the set of common fixed points of finitely many nonexpansive mappings

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

approximating fixed points of nonexpansive mappings in a banach space by metric projections abstract in this paper a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth banach space is proved by using metric projections this theorem is different from the recent strong convergence theorem due to xu h k xu strong convergence of approximating fixed point sequences for nonexpansive mappings bull aust math soc 74 2006 143 151 which was established by generalized projections

inversion of polynomial matrices via state space in this paper the problem of computing inverses of polynomial matrices has been revisited and algorithms of easy implementation are proposed to deal with either column or non column reduced matrices other contributions of the paper are algorithms to perform column reduction and determinant of polynomial matrices

introduction to a newton type method for solving nonlinear equations in this paper we shall introduce a new newton type method namely rational newton for solving a nonlinear equation this new method is shown to converge cubically we shall examine the effectiveness of the rational newton method by comparing the performance with the well established methods namely the classical newton method the halley rational method the kou et al and the weerakoon and fernando method for approximating the root of a given nonlinear equation the approximate solution of the rational newton method is found to be substantially more accurate than the well established methods

relationship between the trace and maximum eigenvalue norms for linear quadratic control design the use of a sum of squares h sub 2 norm is considered for optimal control system design the relative advantages of the linear quadratic gaussian lqg trace norm and the h sub infinity sup norm cost functions are discussed an argument is presented to show that the sum of squares norm ssn problem might be considered alongside the lqg and h sub infinity cost problems when exploring the relationship between the lqg and ssn problems it is found that an lqg controller could be found which correspond to an ssn problem with larger disturbance inputs this suggests that the lqg controller can be computed with the knowledge that it minimizes a well defined ssn problem with worst case uncertainty or disturbances the range of a certain set of eigenvalues is found to provide a measure of the difference between the lqg and ssn problem designs

a new modified secant like method for solving nonlinear equations in this paper we present a new secant like method for solving nonlinear equations analysis of the convergence shows that the asymptotic convergence order of this method is 1 3 some numerical results are given to demonstrate its efficiency

stationary lqg control of singular systems the stationary linear quadratic gaussian control problem is formulated and solved for single input single output singular systems the control system is required to be internally proper and stable in order to avoid both impulsive and unstable exponential behavior the set of all controllers resulting in such a control system is specified in parametric form all controllers that yield finite cost are identified once again in parametric form within this set necessary and sufficient conditions are then established for an optimal controller to exist all optimal controllers are shown to possess the same transfer function the problem is analyzed in the complex domain the transfer functions are expressed as quotients of proper strict hurwitz rational functions by means of this maneuver the powerful tools of algebra are made available the synthesis of the optimal controller is reduced to the solution of two linear diophantine equations whose coefficients are obtained by spectral factorization

numerical solution to a descriptor discrete time algebraic riccati equation abstract we investigate the numerical solution of a special type of descriptor discrete time riccati equation involved in the solution of several key problems in robust control formulated under very general hypotheses necessary and sufficient existence conditions together with computable formulas are given for the stabilizing and antistabilizing solutions in terms of an associated matrix pencil two particular applications and numerical experiments of our results are included for squaring down with l norm preservation and j j spectral factorization both for a completely general discrete time system

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

technical communique all doubly coprime factorizations of a general rational matrix for a general rational matrix function possibly polynomial or improper we give state space formulas for the class of all doubly coprime factorizations over an arbitrary fixed set in the closed complex plane the main result is expressed in terms of a special type of realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the proper case in particular the formulas can be specialized to get the parametrization of all proper polynomial or proper and stable doubly coprime factorizations of an arbitrary descriptor system en route we provide a closed state space formula for the inverse of an invertible general rational matrix

doubly coprime factorization revisited in this note we derive a state space formula for all proper linear time invariant lti doubly coprime factorizations of a given lti plant as an application we present a new derivation of the state space formula for parameterization of all proper lti stabilizing controllers

existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in banach spaces we prove the existence of a solution of the mixed equilibrium problem mep by using the kkm mapping in a banach space setting then by virtue of this result we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of banach spaces by using a projection technique we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of mep and common fixed points set of nonexpansive mappings moreover some applications concerning the equilibrium and the convex minimization problems are obtained

mathcal h _ infty control problem for discrete time algebraic dynamical systems this paper considers the suboptimal mathcal h infty control problem for linear discrete time algebraic dynamical systems such systems can be formally described as linear and time invariant discrete time systems whose transfer function matrix is allowed to be improper or polynomial the parametrization of output feedback controllers is given in a realization based setting involving two generalized algebraic riccati equations and features the same elegant simplicity of the standard proper case two relevant numerical examples prove the effectiveness of our approach

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

perfect observers for singular 2 d fornasini marchesini models a concept of the perfect observer for singular two dimensional 2 d fornasini marchesini models is proposed sufficient conditions are established for the existence of the perfect observer a procedure for design of the perfect observer is also derived and illustrated by a numerical example

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

a weak to strong convergence principle for feje monotone methods in hilbert spaces we consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly exploiting an idea originally proposed by haugazeau we present a simple modification of these methods that makes them strongly convergent without additional assumptions several applications are discussed

new results on doubly coprime fractional representations of generalized dynamical systems this note first points out that the main results by wang and balas regarding the doubly coprime fractional representations for generalized dynamical systems have severe limitation in their applications that is the doubly coprime factorization obtained by wang and balas cannot characterize the parameterization of all properly stabilizing controllers when a system is singular therefore truly generalized to remedy those results two new doubly coprime factorizations have been developed that will parameterize all properly stabilizing controllers for single input or single output cases in addition the new results can characterize the parameterization of all corresponding causal properly stabilizing controllers finally the extension to the multiple input multiple output case is presented

parametrization of ω stabilizing controllers and closed loop transfer matrices of a singular system abstract for a completely general singular system whose transfer matrix may be improper or even polynomial and an arbitrary set in the closed complex plane we give a state space parametrization of all controllers that achieve closed loop transfer matrices having all poles in and of the respective closed loop transfer matrices the main result is expressed in terms of a special type of state space realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the standard proper case in particular the formulas can be specialized to get the parametrization of all controllers that achieve proper polynomial or proper and stable closed loop transfer matrices for a singular system

brief bezout identity related to reduced order observer based controllers for singular systems a design method of causal reduced order observer based controllers for singular systems is presented a new state space representation of the bezout identity for singular systems is developed a parameterization of all causal reduced order controllers is also given the general results given here can be extended to various cases including minimal and full order observer based controllers

model reference predictive lqg optimal control law for simo systems the design of linear quadratic gaussian lqg controllers for single input multiple output simo systems is considered this includes the class of multiloop control problems which are often solved using a classical nested loop structure many simplifications can be achieved over the more general multivariate problem which is important in self tuning control applications for example the tracking problem allows a model following capability to be introduced a predictive control feature is also available which enables the future values of the set point to be taken into account as in preprogrammed robot control

technical communique doubly coprime factorizations related to any stabilizing controllers in state space given a plant and an arbitrary stabilizing controller we present state space formulas for doubly coprime factorizations related to the given controller then we determine parametrizations of all stabilizing controllers centered on that controller

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

h2 optimal control for generalized discrete time systems abstract for a generalized discrete time system whose transfer function matrix may be improper or polynomial we give realization based formulas for the h 2 optimal output feedback controller the formulas bear essentially the same elegant simplicity of the proper case

minimal indices cancellation and rank revealing factorizations for rational matrix functions we study the problem of eliminating the minimal indices the indices of a minimal polynomial basis of the null space of a rational matrix function by multiplication with a suitably chosen invertible rational matrix function we derive the class of all invertible factors that dislocate the minimal indices to certain zero locations and feature minimal mcmillan degree we impose additional conditions on the factor like being j unitary or j inner either with respect to the imaginary axis or to the unit circle and characterize the classes of solutions en route we extend the well known rank revealing factorization of a constant matrix to rational matrix functions the results are completely general and apply in particular to matrices which are polynomial strictly proper or improper rank deficient with arbitrary poles and zeros including at infinity all characterization are made by using descriptor realizations while the associated computations are performed by employing constant unitary transformations and standard reliable procedures for eigenvalue assignment or for solving riccati equations

approximation of common fixed points of a countable family of nonexpansive mappings in a banach space in this paper to find a common fixed point of a family of nonexpansive mappings we introduce a halpern type iterative sequence then we prove that such a sequence converges strongly to a common fixed point of nonexpansive mappings moreover we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator

some variant of newton s method with third order convergence we present a new modification of the newton s method which produces iterative methods with order of convergence three a general error analysis providing the higher order of convergence is given and the best efficiency in term of function evaluations of two of this new methods is provided

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

squaring down by static and dynamic compensators given a system which is not necessarily invertible and which has an unequal number of inputs a method of squaring down that is a method of designing pre compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible is presented the compensators are in general dynamic and have the property that the additional finite zeros induced by them are assignable to the open left half complex plan furthermore the compensators are asymptotically stable and hence do not deteriorate the robustness and performance of an eventual feedback design also the compensator design preserves the stabilizability detectability and minimum phase properties and the infinite zero structure of the original system thus a method of designing nonsquare systems by converting them to square invertible systems is introduced two applications of such a design philosophy 1 diagonal decoupling with state feedback and 2 almost disturbance decoupling with output feedback are pointed out

a robust solution of the generalized polynomial bezout identity in this paper algorithms for the computation of all matrices of the generalized polynomial bezout identity are proposed the algorithms are based on the computation of minimal polynomial basis for the right null spaces of certain polynomial matrices for this reason an algorithm for the computation of minimal polynomial bases is also proposed since this algorithm relies solely on singular value decompositions of certain real matrices formed with the coefficients of the polynomial matrix whose minimal polynomial bases one is interested in finding it can be said to be robust

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces abstract in this paper we introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a banach space then we study the strong and weak convergence of the sequences

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

a general doubly coprime factorization for descriptor systems doubly coprime factorization plays an important role in dealing with multivariable control problems using a factorization approach in this study based on an arbitrary and properly stabilizing controller a general formula of doubly coprime factorization is obtained for use in descriptor systems detailed results have been derived on bridging the factorization approaches previously available in the literature

squaring down with zeros cancellation in generalized systems squaring down with simultaneous zeros cancellation by series compensation of a general possibly polynomial or improper linear system is investigated all static and dynamical compensators that spotlight minimal mcmillan degree are parameterized this general result is particularized to get compensators that preserve the l 2 or l inf norm of the original system either in continuous or discrete time all results are completely general numerically sound and based on general realizations allowing for poles at infinity

strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a hilbert space abstract we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space and then obtain that the sequence converges strongly to a common element of two sets using this result we prove three new strong convergence theorems in fixed point problems variational inequalities and equilibrium problems

doubly coprime matrix fraction representations using proportional and derivative feedback concepts in generalized state space systems the concepts of proportional and derivative state feedback are used to derive some explicit formulas for doubly coprime matrix fraction representations of generalized state space systems specifically proportional and derivative state feedback is used to determine the doubly coprime matrix fraction representations and to solve the corresponding generalized bezout identity in polynomial matrix form

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

h2 output feedback control for descriptor systems this paper solves the h 2 output feedback control problem for continuous time descriptor systems an existence condition of the h 2 optimal controller is derived based on the standard model matching technique and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic riccati equations it turns out that the optimal controller has an observer based structure well known in the state space case so that the results in this paper are natural extensions of the state space results to the descriptor systems a numerical example is also included to show the applicability of the proposed results

a note on h sub 2 optimal control problems with passivity constraints considers the problem of determining the closest function that has a positive real part on the unit disk to a given function in h sub 2 an explicit characterization of the projection is given remarks on potential applications using this projection result to control synthesis and system identification problems are made

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

dual criterion stochastic optimal control problem for robustness improvement the solution of the dual criterion linear quadratic stochastic optimal control problem is obtained by following a wiener type of solution procedure a stabilizing solution is guaranteed by parameterizing the controller using the desoer fractional representation approach the dual criterion includes sensitivity and complementary sensitivity weighting terms which provide a means of varying the robustness characteristics of the multivariable system

doubly coprime fractional representations of generalized dynamical systems explicit formulas for doubly coprime fractional representations of the transfer matrix of a generalized dynamical system are given in terms of a stabilizable and detectable state space realization of the transfer matrix these formulas establish a possible way to use the fractional representation approach in the synthesis of generalized dynamical systems

ℋ2 control of siso fractional order systems abstract in this paper we propose a systematic method to design the optimal 2 output feedback controller for single input single output plants of fractional order based on wiener hopf spectral factorization the plant is allowed to be unstable non minimum phase and incommensurate order using the fractional order youla parameterization the resulting controller satisfies the closed loop internal stability requirement because of the branch point singularities associated with fractional order transfer functions the spectral decompositions are effected via an integral technique an example is provided to demonstrate the design procedure

an algorithm for inverting rational matrices abstract we propose an algorithm for computing the inverses of rational matrices and in particular the inverses of polynomial matrices the algorithm is based on minimal state space realizations of proper rational matrices and the matrix inverse lemma and is implemented as a matlab 1 function experiments show that the algorithm gives accurate results for typical rational matrices that arise in analysis and design of linear multivariable control systems illustrative examples are given

projection and proximal point methods convergence results and counterexamples recently hundal has constructed a hyperplane h a cone k and a starting point y0 in 2 such that the sequence of alternating projections pk ph n y0 n n converges weakly to some point in h k but not in norm we show how this construction results in a counterexample to norm convergence for iterates of averaged projections hence we give an a rmative answer to a question raised by reich two decades ago furthermore new counterexamples to norm convergence for iterates of rmly nonexpansive maps a la genel and lindenstrauss and for the proximal point algorithm al a g uler are provided we also present a counterexample along with some weak and norm convergence results for the new framework of string averaging projection methods introduced by censor et al extensions to banach spaces and the situation for the hilbert ball are discussed as well 2003 elsevier ltd all rights reserved msc 47h09 47j25 90c25

a modification of newton method with third order convergence in this paper we present a new modification of newton method for solving non linear equations analysis of convergence shows that the new method is cubically convergent per iteration the new method requires two evaluations of the function and one evaluation of its first derivative thus the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself its practical utility is demonstrated by numerical examples

a matrix free quasi newton method for solving large scale nonlinear systems one of the widely used methods for solving a nonlinear system of equations is the quasi newton method the basic idea underlining this type of method is to approximate the solution of newton s equation by means of approximating the jacobian matrix via quasi newton update application of quasi newton methods for large scale problems requires in principle vast computational resource to form and store an approximation to the jacobian matrix of the underlying problem hence this paper proposes an approximation for newton step based on the update of approximation requiring a computational effort similar to that of matrix free settings it is made possible by approximating the jacobian into a diagonal matrix using the least change secant updating strategy commonly employed in the development of quasi newton methods under suitable assumptions local convergence of the proposed method is proved for nonsingular systems numerical experiments on popular test problems confirm the effectiveness of the approach in comparison with newton s chord newton s and broyden s methods

eighth order methods with high efficiency index for solving nonlinear equations in this paper we derive a new family of eighth order methods for solving simple roots of nonlinear equations by using weight function methods per iteration these methods require three evaluations of the function and one evaluation of its first derivative which implies that the efficiency indexes are 1 682 numerical comparisons are made to show the performance of the derived methods as shown in the illustration examples

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft

on the wiener hopf approach to optimal feedback design abstract a simple solution is given to the problem of designing a proper feedback which minimizes the h 2 norm of the sensitivity function multiplied by a suitable weighting function

doubly coprime factorizations reduced order observers and dynamic state estimate feedback doubly coprime factorizations of the transfer function of a lumped linear time invariant system are a starting point for many of the results in the factorization approach to multivariabie control system analysis and synthesis in work by nett et al 1984 explicit state space realizations of these factorizations are derived using results from state estimation state feedback theory here new doubly coprime factorizations are developed based on minimal order observers following on from this various extensions are noted and it is proved that the class of all proper stabilizing controllers for a given plant can be generated by dynamic feedback of the reduced order state estimate

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam