poles and zeros at infinity of linear time varying systems the notions of poles and zeros at infinity and their relations are extended to the case of linear continuous time varying systems this study is based on the notion of a newborn systems which is in a mathematical point of view a graded module extension over the noncommutative ring of differential operators it is proved to be a relevant generalization to the time varying case of the equivalence class for the so called restricted equivalence of rosenbrock s polynomial matrix descriptions the authors approach is intrinsic and unifies the definitions previously given in the literature in the time invariant case

robust pole placement design a new technique is presented for the robust design of linear feedback controllers such that the system closed loop poles stay inside a prescribed region in the complex plane despite bounded plant parameter variations the method is based on the definition of a robust measure for any given controller and on the search by an iterative method for the controller which maximizes that measure

stability of polynomials under coefficient perturbation let the real polynomial a 0 x n a 1 x n 1 a n 1 x a n be stable and let the real numbers b k c k geq 0 0 leq k leq n be given we present a simple determinant criterion for finding the largest t 0 geq 0 such that the polynomial alpha 0 x n alpha 1 x n 1 alpha n 1 x alpha n is stable for all alpha k in a k b k t 0 a k c k t 0 cup a k 0 leq k leq n several further observations allow us to reduce the computational cost considerably

on the computation of proper feedforward internally stabilizing and pole placing compensators by combining two important results from the polynomial and fractional representation approaches we derive a state space formula for the direct computation of a proper feedforward internally stabilizing and pole placing compensator c s

system theoretic based characterisation and computation of the least common multiple of a set of polynomials abstract the paper provides a system theoretic characterisation of the least common multiple lcm m s of a given set of polynomials p which leads to an efficient numerical procedure for the computation of lcm that avoids root finding and use of greatest common divisor gcd procedures the procedure that is presented also leads to the computation of the associated set of multipliers of p with respect to lcm the basis of the new characterisation and computational procedure are the controllability properties of a natural realization s a b c associated with the set p it is shown that the coefficients of the lcm are defined by the properties of the controllable subspace of the pair a b which also leads to the characterisation of associated multipliers an algorithmic procedure that exploits the companion structure of a is formulated and its numerical properties are investigated the new method provides a robust procedure for the computation of lcm and enables the computation of approximate values when the original data are innacurate

polynomial matrix linearization and strongly irreducible realization for singular systems abstract a scheme for polynomial matrix linearization is proposed by using the linearization we propose a realization for singular systems the properties of the realization are studied and then a strongly irreducible realization is presented

directed structure at infinity for infinite dimensional systems in this article the structure at infinity of infinite dimensional linear time invariant systems with finite dimensional input and output spaces is discussed it is shown that a diagonal form describing behaviour near infinity can be found this diagonal form is a generalisation of the smith mcmillan form at infinity for rational matrices it is then used to simplify certain solvability conditions of a regulation problem examples on time delay and distributed parameter systems are given

generalized proper inverse of polynomial matrices and the existence of infinite decoupling zeros a necessary and sufficient condition is presented for the existence of a generalized proper rational inverse for nonsquare polynomial matrices the condition is then proved to be equivalent to the absence of infinite decoupling zeros this condition provides a simple test for the absence of infinite decoupling zeros in the polynomial fraction form it can also be used to remove the infinite decoupling zeros in order to achieve a strongly irreducible system and to provide a new look of the unimodular matrix operation effect at infinity for the left and right polynomial fraction forms

stability analysis of interval matrices another sufficient condition a sufficient condition for the stability of interval matrices is presented based on a lyapunov approach the condition while requiring the solution of a lyapunov matrix equation removes the restrictions imposed by heinen 1984 examples given illustrate the improvement of the proposed condition over the ones given by heinen and bialas 1983 and daoyi 1985

infinite frequency structure and a certain matrix laurent expansion abstract a method for determining the smith mcmillan form at infinity of a rational matrix is derived by considering the laurent expansion at infinity of the matrix this method is used to provide a new test for the absence of infinite zeros in a rational matrix and a new formula for calculating the highest degree among the largest minors of a polynomial matrix

minimal delay fir delayed left inverses for systems with zero nonzero zeros abstract this paper considers finite time input reconstruction for discrete time linear time invariant systems in the case where the initial condition is unknown there are three main results first a specific construction of finite impulse response fir delayed left inverse with the minimal delay for systems with zero nonzero zeros is presented next it is shown that in the presence of an arbitrary unknown initial condition finite time input reconstruction is possible using a delayed left inverse h if and only if h is fir finally it is shown that a transfer function with full column normal rank has an fir delayed left inverse with the minimal delay if and only if the system has zero nonzero zeros

characterization of robust controllers abstract this paper presents a procedure for designing a robust controller which is able to stabilize a multivariable system with interval uncertainties in the system parameters the uncertain parameters are assumed to lie within known intervals the fundamental idea behind the procedure is to characterize the set of robust controllers as a convex set by the new matrix inequalities result a suitable controller can then be chosen by means of an optimization algorithm the controller thus chosen will be able to ensure that the closed loop matrix lies within desired intervals for all the prescribed interval uncertainties in the system parameters

necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure this correspondence is concerned with an image f b sup m of a box b sup m spl sub r sup m under a multiaffine transformation f r sup m spl rarr c the authors introduce a notion of a principal point of b sup m and prove that the boundary of f b sup m is covered by images of principal points the authors exploit this result to provide necessary and sufficient robust stability conditions for polynomials whose coefficients are multiaffine functions of parameters an application of the general criterion obtained in the correspondence to the particular case of systems with a cascade of first order uncertain blocks leads to a computationally tractable procedure that verifies stability of the systems

pole placement for singular systems abstract in this paper we present a pole placement design for singular systems in polynomial fraction form the design can also be used for the role placement of singular systems in generalized state space form and requires no decomposition

a closed formula for the determination of the impulsive solutions of linear homogeneous matrix differential equations a closed formula is given which allows the determination of the impulsive solutions of linear homogeneous matrix differential equations lhmde directly in terms of finite and infinite spectral data of the associated polynomial matrix specifically the notions of finite and infinite jordan pairs for a general polynomial matrix are defined and it is pointed out the strong relationship among them and the impulsive solutions of lhmde

brief paper assigning closed loop invariant polynomials over polytopes for linear periodic systems this paper provides a parameterization of all output feedback periodic controllers providing closed loop invariant polynomials varying over some assigned polytopes for linear discrete time periodic plants using the notion of time invariant system associated to a periodic system the parameterization is provided in terms of the general solution of a suitably defined matrix diophantine equation

optimal lipschitzian selection operator in quasi convex optimization abstract given a bounded real function f defined on a closed bounded real interval i the problem is to find a quasi convex function f which minimizes the supremum of f s f s for all s in i over the class of all quasi convex functions f on i such a nearest function f is not unique in general for each f is it possible to select a nearest f so that the selection operator f f satisfies a lipschitz condition with some constant c if so does there exist an operator for which c is minimum it is shown that there exists a maximal nearest function f so that the operator f f is such an optimal lipschitzian selection operator with c 2

assigning invariant polynomials over polytopes this paper provides a parameterization of all output feedback controllers yielding closed loop invariant polynomials varying over some assigned polytopes

an algorithm for robust pole assignment via polynomial approach a computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented the analysis is based on transfer functions of characteristic polynomials and the problem is formulated as one of semi infinite programming an example of an application is given to illustrate this approach

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

on the selection of poles in the single input pole placement problem abstract it is well known that the single input pole placement problem can be quite sensitive to perturbations in the data recent results by mehrmann and xu show how this sensitivity depends on the location of the poles in many applications it suffices to prescribe a set k in the complex plane that contains the poles mehrmann and xu formulated a minimization problem for allocating the poles in a given set k so that the sensitivity to perturbations is reduced the present paper uses methods of potential theory to derive simple algorithms that yield approximate solutions of this minimization problem

strong stabilization over polytopes the problem considered consists of finding a stable controller assigning a closed loop characteristic polynomial over a stability domain specified as a polytopic region of the space of characteristic polynomial coefficients the controller is required to be stable with respect to the same polytopic stability region specified for the closed loop system

simultaneous partial pole placement a new approach to multimode system design simultaneous partial pole placement of a family of single input single output plants is proposed as a generalization of the classical pole placement and stabilization problems this problem finds application in the design of a compensator for a family of linear dynamical systems in this note we show that the proposed problem is equivalent to a new class of transcendental problem using stable minimum phase rational functions with real coefficients a necessary condition for the solvability of the associated transcendental problem is obtained finally a counterexample to the following conjecture is obtained pairs of simultaneously stabilizable plants of bounded mcmillan degree have simultaneously stabilizing compensators of bounded mcmillan degree

structure smith macmillan form and coprime mfds of a rational matrix inside a region p ω abstract the structure of the smith macmillan form of a rational matrix t s inside a region p where is asymmetric with respect to the real axis subset of the finite complex plane c is determined algorithmic procedures based on elementary row and column operations over the euclidean ring r p s consisting of all rational functions with no poles in p are given coprimeness in p of a pair of rational matrices is studied in detail these results lead to constructive procedures for determining the coprime in p matrix fraction descriptions of t a

a class of multilinear uncertain polynomials to which the edge theorem is applicable this paper gives a class of multilinear uncertain polynomials to which the edge theorem is applicable in the paper a notion of symmetric uncertainty structure is introduced the main result is as follows if a multilinear uncertain polynomial has a symmetric uncertainty structure and the uncertain parameters are nonoverlapping then the corresponding value sets will be convex polygons this means that the use of the zero exclusion condition to test the robust stability of such uncertain polynomials is feasible since we need only to calculate the extreme points of the convex polygons furthermore a version of the edge theorem can be used to test the robust stability of such uncertain polynomials

perturbation bounds for robust stability in linear state space models abstract this paper addresses the aspect of stability robustness of linear systems in the time domain upper bounds on the linear perturbation of an asymptotically stable linear system are obtained to maintain stability both for structured as well as unstructured perturbations using the lyapunov approach for structured perturbation the resulting bound is such that it garners the structural information about the nominal as well as the perturbation matrix into a single unified expression in the case of unstructured perturbations special features of the nominally stable matrix are exploited resulting in simpler expressions for the bound without the need to solve the lyapunov equation improvement of the proposed measures is illustrated with the help of examples

denominator assignment invariants and canonical forms under dynamic feedback compensation in linear multivariable systems a result originally reported by hammer for linear time invariant lti single input single output systems and concerning an invariant and a canonical form of the transfer function matrix of the closed loop system under dynamic feedback compensation is generalized for lti multivariable systems based on this result we characterize the class of transfer function matrices that are obtainable from an open loop transfer function matrix via the use of proper dynamic feedback compensators and show that if the closed loop transfer function matrix pc s has a desired denominator polynomial matrix which satisfies a certain sufficient condition then there exists a proper compensator giving rise to an internally stable closed loop system whose transfer function matrix is pc s

generalized state space realizations from matrix fraction descriptions the problem of the realization of a matrix fraction description mfd of a nonproper transfer function is considered an algorithm for the realization is developed and it is shown that it is a natural generalization of wolovich s method 1973 for the case of proper systems the resulting generalized state space system is shown to be reachable and the conditions for its minimality in terms of the coprimeness and column reducedness of the mfd are derived the relation between the controllability indexes of the realization and the forney order 1975 of the mfd is established

a note on robust pole placement pole placement algorithm in single input single output siso systems is discussed with respect to the corresponding real stability radius of the resulting closed loop polynomial

robust stability and robust pole assignment of linear systems with structured uncertainty sufficient conditions for the robust stability of linear time varying systems are presented the stability criteria are extended to the problem of the robust pole assignment of linear time invariant systems to a specified region these criteria both for robust stability and robust pole assignment improve some results in the literature examples are given to demonstrate the new criteria

equivalence transformations of rational matrices and applications the known theories of transformations between polynomial matrices are extended to the case of rational matrices specifically equivalence between rational matrices having possibly different dimensions is defined and this has the property of preserving the zero structure of rational matrices in the region c some implications of this new equivalence transformation for linear system theory are also provided

characterization of allowable perturbations for robust stability the problem of determining stability for a closed loop linear multivariable process in the presence of ill defined process perturbations is considered it is shown that m matrices may be used to characterize a class of allowable perturbations

relations between strict equivalence invariants and structure at infinity of matrix pencils the structure at infinity of matrix pencils is investigated via their smith macmillan forms at infinity 1 relations between some strict equivalence invariants and pole zero structure at infinity are established

the exact model matching problem for linear time varying systems an algebraic approach the exact model matching problem is formulated and solved for linear time varying systems the condition for the existence of a proper solution which is well known in the time invariant case is proven here to still be valid in the time varying case the properness is characterized using the smith macmillan form at infinity recently defined by the authors for the transfer matrices with time varying coefficients

cascade control of systems over integral domains necessary and sufficient conditions for the existence of cascade compensators and dynamic equivalence of linear systems over integral domains arc derived the considerations lead to constructive procedures for dynamic compensation

computation of the inverse of a polynomial matrix and evaluation of its laurent expansion abstract an algorithm is given which constitutes a generalization of the algorithm for the inversion of a pencil se a due to mertzios 1984 in the case of general systems described in differential operator form recursive formulae are obtained for the calculation of both the coefficient matrices of the adjoint of the polynomial matrix as well as for the coefficients of the characteristic polynomial of the polynomial matrix a simple method is also presented that allows the evaluation of the laurent expansion for the inverse of a polynomial matrix of any order specifically an arma model is given for the computation of the coefficient matrices of the laurent expansion in terms of the coefficient matrices of the polynomial matrix without inverting the latter the laurent expansion of a polynomial matrix is used for the analysis and synthesis of the polynomial matrix descriptions that constitute a further generalization of the singular or generalized systems

a new approach to the optimization of envelope constrained filters with uncertain input in envelope constrained filtering the filter is optimized subject to the constraint that the filter response to a given signal lies within a specified envelope or mask in a number of signal processing applications the envelope constrained filtering problem is more directly relevant than least squares approximation based approaches the present authors develop an efficient method for solving an extended version of the envelope constrained filtering problem in which the input pulse is not known exactly but is known to lie within a specified mask this envelope constrained problem with uncertain input ecui has been examined elsewhere but the algorithm proposed there for its solution has in general inferior convergence characteristics

on pole structure assignment in linear systems the problem of pole structure assignment psa by state feedback in implicit linear and uncontrollable systems is discussed in the article it is shown that the problem is solvable if the system is regularisable then necessary and sufficient conditions for characteristic polynomial assignment are established in the case of psa invariant polynomials assignment just necessary conditions have been obtained but it turns out that these conditions are also sufficient in some special cases this happens for example when the system does not possess any non proper controllability indexes a possible application of the achieved results to modelling a constrained movement of a robot arm is outlined too

characterization of allowable perturbations of a closed loop system with pole placement controller the problem of determining stability of a closed loop transfer function in the presence of coefficient perturbations is considered the results of interval polynomial theory are used to characterize the allowable interval of variation

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

design of precompensators via infinite zero structure for dynamic decoupling of linear invertible systems the problem of designing precompensators necessary for decoupling invertible systems having weak inherent coupling is considered a simple algorithm which is directly applicable to systems characterized by square proper transfer function matrices t s is proposed for such design in the proposed algorithm the concept row reducedness at infinity of t s is utilized as an alternative necessary and sufficient condition for the decouplability of t s in addition to the simple design procedure of the compensator the algorithm yields the infinite zero structure of both t s and the resulting compensated system

ellipsoidal approximation of the stability domain of a polynomial the stability domain in the space of coefficients of a polynomial is a nonconvex set in general in this note we propose a new convex ellipsoidal inner approximation of this set derived via optimization over linear matrix inequalities as a by product we obtain new simple sufficient conditions for stability that may prove useful in robust control design

time optimal output regulators for linear multivariate discrete time systems part 2 all classes of right invertible systems in part 1 of this paper hassan and amin 1987 a simple algebraic solution for the time optimal output regulator problem was presented this solution which consists of a state feedback control law has been obtained for all classes of right invertible decouplable systems s a b c e the results of part 1 are here extended to all classes of right invertible systems s a b c e a set of optimal output deadbeat indices called the optimal set is defined and related to the observability indices of the optimal closed loop system the time optimal output regulator problem for a right invertible non decouplable system s a b c e is resolved by transforming s into a decouplable system sc a b cc ec having the optimal output deadbeat index of s first an algorithm is presented to construct iteratively in a well defined optimal sense a unimodular left compensator l z and a compensated decouplable system sc a b cc ec from the state space parameters of s then a family of optimal state fee

computation of finite and infinite zeros of linear multivariable systems a state space approach an iterative algorithm developed by the authors to compute the finite zeros of a linear multivariable system sebakhy et al 1983 is extended to compute the infinite zeros of the system as well the method is simple efficient and suitable for programming on a digital computer

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

dynamic compensation of siso systems over a principal ideal domain the polynomial equation approach and some concepts from algebraic geometry are employed in compensator design for a class of linear single input single output siso systems with coefficients from a principal ideal domain pid

an o n algorithm for least squares quasi convex approximation this article is concerned with the approximation problem of fitting n data points by a quasi convex function using the least squares distance function an algorithm of o n worst case time complexity for computing a best fit is developed this problem arises in the context of curve fitting or statistical estimation

robust characteristic polynomial assignment abstract in this paper a computational method for designing controllers which attempt to place the characteristic polynomial of an uncertain system inside some prescribed region is presented an objective function consisting of two terms is proposed penalizing both the distance to a given controller and the size of the uncertainty region developed to solve the robust assignment problem the algorithm is based on semi infinite programming theory and the special structure of the problem is exploited to get both simpler methods and convergence proof the way in which the uncertain parameters affect the plant coefficients is realistic since it includes multinomial dependence an example of application is given to illustrate the approach

multivariate root locus behaviour and the relationship to transfer function pole zero structure this paper is concerned with the qualitative behaviour of the multivariable root locus for high and low gains for a non singular m m rational transfer function the butterworth approach and departure patterns are shown to be determined in all cases by the zeros and poles of certain algebraic functions these are in turn characterized at each point of the extended complex plane by a set of m rational numbers called the root locus indices in addition the smith mcmillan pole zero structure of the transfer function is represented at each point of the extended complex plane by a sequence of m integers called the mcmillan indices an algebraic condition for the coincidence of the two sets of indices is established using the algebraic function theory underlying the newton diagram method together with a valuation characterization of the smith mcmillan form it is shown directly without simple null structure assumptions or equivalent conditions on constant matrices that the condition is generically met

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

proper rational matrix diophantine equations and the exact model matching problem relying on the theory behind the smith macmillan form of a rational matrix at s infty a necessary and sufficient condition is derived from the solvability of matrix diophantine equations of the form a s x s b s y s m s where a s b s and m s are given proper rational matrices and x s and y s are unknown proper rational matrices it is shown that the above result can be used in order to resolve in a new illuminating way the exact model matching problem emmp if a solution to emmp exists then the family of all solutions is parametrized

refined schur method for robust pole assignment with repeated poles schur type methods in 6 and 11 solve the robust pole assignment problem by employing the departure from normality of the closed loop system matrix as the measure of robustness they work well generally when all poles to be assigned are simple however when some poles are close or even repeated the eigenvalues of the computed closed loop system matrix might be inaccurate in this paper we present a refined schur method which is able to deal with the case when some or all of the poles to be assigned are repeated more importantly the refined schur method can still be applied when place 14 and robpole 28 fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom

decentralized diagonal dynamic stabilization of linear multivariable systems abstract the diagonal stabilization problem dsp is defined over the ring of proper rational functions which have no poles inside a prescribed region of the finite complex plane solvability is intimately related to systems which exhibit the property of cyclicity necessary and sufficient conditions are established for the existence of solutions to the dsp a complete parametrization of stabilizing controllers for the 2 2 case is given conditions of nonsolvability and hence nonstabilizability yield an explicit expression for the fixed modes of the system

sensitivities of stability constraints and their applications let the real polynomial a s a 0 a 1 s a n s n with the coefficients being known differentiable functions a k x be given and let the constraints g i x 0 determine the strictly hurwitz property of the polynomial a s a simple and efficient method to calculate the derivatives partial g i x partial x j is proposed then the application of the method to the problem of stability of polynomials under coefficient perturbation by gradient optimization is discussed also a theorem characterizing the stability region and the newly introduced regions of nondestabilizing perturbations is given

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

numerical methods in control we study classical control problems like pole assignment stabilization linear quadratic control and h control from a numerical analysis point of view we present several examples that show the difficulties with classical approaches and suggest reformulations of the problems in a more general framework we also discuss some new algorithmic approaches

algebraic and dynamic characterizations of poles and zeros at infinity abstract the presence of infinite frequency poles and zeros in a rational transfer function matrix is considered and certain algebraic characterizations for their occurrence are given one such characterization is shown to enable the transmission effects due to infinite poles and zeros to be ascertained in an extremely simple and direct way

robust pole assignment abstract this paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots and applies them to the problem of robust pole placement we formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed loop poles within desired intervals for plants with unknown but bounded parameter uncertainties the algorithms are computationally reasonable and provide a useful addition to currently existing control cad tools

internal stabilization and decoupling in linear multivariable systems by unity output feedback compensation we consider the problem of internally stabilizing and simultaneously diagonally decoupling a linear multivariable system by unity output feedback compensation a sufficient condition is derived for the existence of a cascade proper compensator c s such that when employed in a unity feedback loop involving the proper transfer function matrix p o of a free of unstable hidden modes system sigma p o will not only internally stabilize the feedback closed loop system sigma p o c but will also give rise to a closed loop transfer function matrix h yr diag which is nonsingular diagonal and has desired poles based on this analysis an algorithmic procedure for the computation of such a compensator is presented

quasi convex optimization given a bounded real function f defined on a closed bounded real interval i the problem is to find a quasi convex function f so as to minimize the supremum of f s f s for all s in i over the class of all quasi convex functions f on i this article obtains optimal solutions to the problem and derives their properties this problem arises in the context of curve fitting or estimation

the robust root locus abstract in this paper a simple technique is described for generating the root loci of a feedback system which includes perturbations q rl entering affine linearly into the coefficients of the plant denoting the perturbed plant by p s q and the compensator by c s we address the following problem given a bounding set q rl for q find the locus of points z in the complex plane such that 1 kp z q c z 0 for some k 0 and some q q such points z are said to lie on the robust root locus one of the strengths of the technique presented in this paper is that it avoids the combinatoric explosion synonymous with gridding the l dimensional set q and plotting a large number of ordinary root loci associated with gridding the points instead the technique given here exploits only a 2 dimensional gridding of a bounded subset of the complex plane for the more general case when perturbations enter multilinearly into the coefficients a certain convex hull robust root locus is constructed finally the robust root locus technique is illustrated using a model of a supersonic transport plane

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

classification of proper bases of rational vector spaces minimal macmillian degree bases abstract the algebraic structure of the get of all proper rational vectors contained in a given rational vector space x1d4af s is shown to be that of a noothorian pr s motiulo m ropf pr a is the ring of proper rational functions the proper submodules mt of m form an ascending chain of submodules partially ordered by an invariant of mt defined as the valuation at s ofmt tho various bases of mt are examined and classified according to their property of column reduceness at s the concept of a prime column reduced at basis of mt is introduced it is shown that tho prime bases of mt can be further classified by their macmillan degrees and the existence of minimal macmillan degree bases for mt is established a prime and minimal macmillan degree basis ofmt extends forney s concept of a minimal polynomial basis of s for the rpr mt module the macmillan degrees of the columns of such bases form a set of invariants mt for which are defined as the x1d4af s generalized invariant dynamicol indices o

technical communique robust stability and performance with fixed order controllers this paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order for a linear time invariant plant for a fixed plant as well as for an uncertain family of plants containing parameter uncertainty so that stability robust stability and robust performance are attained the desired closed loop specifications considered here are given in terms of a target performance vector representing a desired closed loop design in general these point targets are unattainable with a fixed order controller by enlarging the target from a fixed point set to an interval set the solvability conditions are relaxed and a solution is enabled results from the parametric robust control literature can be used to design the interval target family so that the poles and zeros of the closed loop system are guaranteed to remain in a prescribed region of the complex plane and closed loop performance measured for instance in the h norm are attained even when plant uncertainty is present it is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications the approach developed here gives the entire set of controllers attaining the specifications as a convex set and also can be recast to give the lowest order controller attaining specifications

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

robust stability under a class of nonlinear parametric perturbations this paper considers the robust stability verification of linear time invariant systems admitting a class of nonlinear parametric perturbations the general setting is one of determining the closed loop stability of systems whose open loop transfer functions consist of powers products and ratios of polytopes of polynomials apart from this general setting two special cases of independent interest are also considered the first special case concerns uncertainties in the open loop gain and real poles and zeros while the second special case treats uncertainties in the open loop gain and complex poles and zeros in light of the zero exclusion principle robust stability is equivalent to zero exclusion of the value sets of the system characteristic function a value set consists of the values of the characteristic functions at a fixed frequency the main results of this paper are as follows 1 the value set of the characteristic function at each fixed frequency is determined by the edges and some frequency dependent internal line segments 2 consequently hurwitz invariance verification simplifies to that of checking certain continuous scalar functions for avoidance of the negative real axis 3 for the case of real zero pole gain variations the critical lines are all frequency independent and therefore the determination of the robust stability is even simpler 4 for the case of complex zero pole gain variations the critical internal lines are shown to be either frequency independent or to be confined in certain two dimensional planes or three dimensional boxes

a new method for computing the stable invariant subspace of a real hamiltonian matrix abstract a new backward stable structure preserving method of complexity o n3 is presented for computing the stable invariant subspace of a real hamiltonian matrix and the stabilizing solution of the continuous time algebraic riccati equation the new method is based on the relationship between the invariant subspaces of the hamiltonian matrix h and the extended matrix 0 h h 0 and makes use of the symplectic urv like decomposition that was recently introduced by the authors

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

some local results for linear systems and implications for state variable feedback a result concerning the invariance of the infinite zero structure of a general transfer function matrix under state feedback is obtained the approach indicates the need for a localized theory of linear systems and some basic results in this area are derived a surprising property of the infinite pole structure is also revealed