output feedback stabilization for uncertain systems constrained riccati approach in this paper the problem of output feedback stabilization of linear systems with mismatched uncertainties is investigated a new approach to the design of output feedback controller is proposed and the respective output feedback gains are obtained through the solution of a riccati equation with linear constraints solvability conditions for such a constrained riccati problem are derived and a systematic algorithm for obtaining an output feedback controller which guarantees the system state is globally exponentially stable is provided

the laguerre and legendre polynomials from an operational point of view the use of the monomiality principle and of the associated operational calculus allows to reformulate the theory of laguerre and legendre polynomials from a unified point of view they are indeed shown to be particular cases of more general polynomials whose usefulness in purely mathematical and applied contexts is discussed the concepts introduced in the paper are also exploited to develop an elementary point of view on the theory of legendre and laguerre bessel functions

connection coefficients between boas buck polynomial sets abstract in this paper a general method to express explicitly connection coefficients between two boas buck polynomial sets is presented as application we consider some generalized hypergeometric polynomials from which we derive some well known results including duplication and inversion formulas

comments on output feedback stabilization for uncertain systems constrained riccati approach for original paper by cheng see ibid vol 43 p 81 4 1998 in that paper a sufficient condition for the static output feedback stabilization of uncertain systems with mismatched uncertainties has been derived under the assumption that rank b spl les rank c where b and c are the input matrix and the output matrix respectively in this note we show that the sufficient condition of the original paper is not solvable if rank b rank c and thus the result of the above paper is valid only for the case of rank b rank c

stabilization of an uncertain linear dynamic system by state and output feedback a quadratic stabilizability approach in this paper the output control problem for linear uncertain systems is investigated under the specific framework of quadratic stabilizability the approach generalizes previous works to systems where both the state and input matrices suffer from structural uncertainty of norm bounded as well as interval type the stabilizability conditions are translated into parametrical problems the output stabilizability problem both in the static and dynamic aspects is investigated with the help of quadratic stabilizability and its dual notion the quadratic detectability the dynamic output stabilization problem can first be formally expressed as a static one in this case the proposed approach does not enable us to deal with the complete uncertainty case where all the dynamic control and output matrices are uncertain the output dynamic compensation in the classical framework of observer design is also addressed

on the natural vibrations of linear structures with constraints the undamped natural vibrations of a constrained linear structure are given by the solutions to a generalized eigenvalue problem derived from the equations of motion for the constrained system involving lagrangian multipliers the eigenvalue problem derived is defined by the mass matrix of the unconstrained structure and a non symmetric and singular stiffness matrix for the constrained system the character of the solution of the eigenvalue problem of the constrained system is stated and proved in a theorem applications of the constrained eigenvalue problem to some simple structures are demonstrated finally a condition for the calculation of the damped natural vibrations for the constrained structure in terms of the undamped mode shapes is formulated

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

an orthogonal decomposition approach to modal synthesis modal synthesis is a method of formulating the equations of motion for complex vibratory systems this approach has many advantages in modelling systems that consist of an assembly of linear dynamic elements whose modal characteristics are given presented in the paper is a procedure for synthesizing linear dynamic models into one dynamic description in a numerically stable way this task is achieved by an orthogonal co ordinate transformation replacing the matrix inversions required when other procedures are used the modal synthesis approach is formulated as a problem of finding the equations of motion for a linear system subject to a set of linear constraints the numerical procedure to generate the equations of motion in terms of independent co ordinates is presented the paper concludes with several examples that demonstrate the properties of the proposed method and its application to the modelling of vibratory systems

differential and integral equations for the 2 iterated appell polynomials in this article a set of differential equations of finite order k th order k n for the 2 iterated appell polynomials are derived particular cases k 1 and k 2 are also considered the integral equations for the appell and 2 iterated appell polynomials are established further as an illustration the differential and integral equations for the 2 iterated generalized bernoulli polynomials are derived this article is first attempt in the direction of deriving integral equations for the appell and 2 iterated appell families and for some members belonging to these families

sufficient lmi conditions for output feedback control problems the authors present linear matrix inequality lmi conditions for output feedback control problems the results are based on sufficient conditions because they are dependent on the particular state space representation used for describing the system nevertheless the conditions are not sensitive to a certain class of state space transformations and if the control problem is feasible then there exists some state space transformation leading the conditions to be necessary and sufficient for the problem the authors approach can be used for designing decentralized controllers and is easily extended to h sub 2 h sub spl infin and mixed h sub 2 h sub spl infin problems via standard lmi techniques the continuous and discrete time cases are considered and numerical examples are given to illustrate the results

connection problems via lowering operators the lowering operator associated with a polynomial set pn n 0 is an operator not depending on n and satisfying the relation pn npn 1 in this paper we express explicitly the connection coefficients between two polynomial sets using their corresponding lowering operators we obtain some well known results as particular cases including some duplication and addition formulas

a set of finite order differential equations for the appell polynomials let r n x n 0 denote the set of appell polynomials which includes among others hermite bernoulli euler and genocchi polynomials in this paper by introducing the generalized factorization method for each k n we determine the differential operator l n k x n 0 such that l n k x r n x l n kr n x where l n k n k n k the special case k 1 reduces to the result obtained in m x he p e ricci differential equation of appell polynomials via the factorization method j comput appl math 139 2002 231 237 the differential equations for the hermite and bernoulli polynomials are exhibited for the case k 2

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

nonquadratic lyapunov functions for robust stability analysis of linear uncertain systems in this note we derive conditions of existence of a homogeneous polynomial lyapunov function of an arbitrary even degree establishing global asymptotic stability of linear system with box bounded uncertainty verification of these conditions is reduced to solving a convex minimization problem we produce numerical examples that demonstrate significant improvement in estimates of admissible uncertainty bounds compared with estimates obtained via the most commonly used quadratic lyapunov functions

factorization of self adjoint ordinary differential equations this paper deals with the factorization of self adjoint differential operators l 2 n email protected ndx email protected b nd ndx n and their spectral type differential equations sufficient conditions of factorization are reported a large class of differential operators and equations that can be factorized is obtained the factorizations of fourth and sixth order operators and equations are explicitly given a particular fourth order spectral type differential equation in which r x 1 x p 1 x q p 1 q 1 is considered its general solution is obtained in terms of hypergeometric functions as application the natural frequencies and mode shapes of mechanical transverse vibrations of a nonuniform structure are found

laguerre type special functions and population dynamics abstract we introduce new laguerre type population dynamics models these models arise quite naturally by substituting in classical models the ordinary derivatives with the laguerre derivatives and therefore by using the so called laguerre type exponentials instead of the ordinary exponential the l exponentials e n t are increasing convex functions for t 0 but increasing slower with respect to exp t for this reason these functions are useful in order to approximate different behaviors of population growth we consider mainly the laguerre type derivative d t t d t connected with the l exponential e 1 t and investigate the corresponding modified logistic bernoulli and gompertz models invariance of the volterra lotka model is mentioned

brief paper decentralised static output feedback stabilisation and synchronisation of networks in this paper global stabilisation of a complex network is attained by applying local decentralised output feedback control to a minimum number of nodes of the network the stabilisation of the network is treated as a rank constrained problem strict positive realness conditions on the node level dynamics allow nonlinearities uncertainties which satisfy the sector conditions to be considered a network of chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach

on the stabilization and observation of nonlinear uncertain dynamic systems the problem of stabilization and observation of uncertain and or nonlinear dynamic systems for which matching conditions are not satisfied is investigated no statistical description of uncertain elements is assumed the uncertain and or nonlinear quantities are described only in terms of bounds on their possible sizes stabilizing feedback controllers and observers are proposed whose design is based on the constructive use of lyapunov functions and the bellman gronwall lemma

a matrix approach to some identities involving sheffer polynomial sequences a simple but elegant method was adopted in youn and yang 2011 in order to derive a differential equation and recursive formulas for sheffer polynomials namely they used the so called the generalized pascal functional matrix of an analytic function and the wronskian matrix of several analytic functions in this paper we will use their method to find some identities satisfied by sheffer polynomials

one approach to the control of uncertain dynamical systems we present a controller design methodology for uncertain systems which is based on the constructive use of lyapunov stability theory the uncertainties which are deterministic are characterized by certain structural conditions and known as well as unknown bounds as a consequence of the lyapunov approach the methodology is not restricted to linear or time invariant systems the robustness of these controllers in the presence of singular perturbations is considered the situation in which the full state of the system is not available for measurement is also considered as are other generalizations

vibration of modified discrete systems the modal constraint method in an earlier paper 1 a method was presented for calculating eigenfrequencies and modes of a vibrating system whose modifications consist of adding point supports in another paper 2 generalization of the method of reference 1 was presented for establishing vibration characteristics for complex continuous systems which are composed of several base or known continuous systems in this paper this method the modal constraint method is applied to discrete systems the eigenfrequencies and modes of the base systems calculated with the aid of for instance the finite element method are used to established the vibrational characteristics of the modified systems the modifications may consist of addition or removal of base systems and or adding supports the reduction of work as compared with direct solving of the modified system problems is significant especiallyfor large degree of freedom problems

a determinantal approach to appell polynomials a new definition by means of a determinantal form for appell 1880 1 polynomials is given general properties some of them new are proved by using elementary linear algebra tools finally classic and non classic examples are considered and the coefficients calculated by an ad hoc mathematica code for particular sequences of appell polynomials are given

stabilizability conditions of multivariable uncertain systems via output feedback control a stabilizability condition is established for stabilizing multivariable uncertain dynamical systems with matched uncertainties by linear static output feedback control it is shown that under the assumptions of minimum phase and nonsingular high frequency gain for the nominal plant stabilization with linear static output feedback control is achievable a necessary and sufficient condition is also obtained for the existence of constant output feedback which makes the closed loop system strictly positive real

robust linear controllers using observers the possibility of determining a linear robust control law when the full state cannot be measured and observers are implemented to estimate the state is considered the focus is on systems where the uncertainty satisfies the matching condition the control law and the observer are designed using two riccati equations the first result establishes that if certain scalar parameters are chosen so that a matrix inequality is satisfied the closed loop system is stable for the uncertainty levels of interest it is then shown that if there are at least as many sensors as there are actuators and the transfer function of the nominal system or a squared down form of it does not have zeros in the closed right half plane the closed loop system can be stabilized by the technique regardless of the size of the uncertainty bounding set

d orthogonality via generating functions in this paper starting from a suitable generating function of a polynomial set we show how to decide whether the considered polynomial set is d orthogonal and if it is so how to determine the corresponding d dimensional functional vector then we apply the obtained results to some known and new d orthogonal polynomial sets for the known ones we give new proofs for some already obtained results

operational rules and a generalized hermite polynomials in this paper we use operational rules associated with three operators corresponding to a generalized hermite polynomials introduced by szego to derive as far as we know new proofs of some known properties as well as new expansions formulae related to these polynomials

robust stability of lure systems with multiple nonlinearities the stability of a perturbed lure system is studied through the popov lyapunov approach the multivariable popov criterion is used to guarantee the stability of the nominal system and then the stability of the perturbed system is investigated by using the lyapunov function developed for the nominal system a robustness measure which gives some bounds on allowable perturbations for the system is derived evading the use of norm forms a feature of the proposed measure is that the observation of the range for individual parameter deviation is feasible

vibration of complex structures the modal constraint method abstract a method is described for establishing the natural frequencies of an arbitrary structure with arbitrary supports the method is based on the modal constraint technique described in a previous paper 1 as shown in the present paper weinstein s theory for the intermediate problem can be regarded as equivalent to the lagrangian multiplier method i e both methods result in the same eigenvalue equations weinstein s theory deals with modifications of base differential operators whereas the lagrangian multiplier method deals with modifications of base energy functionals the modal constraint technique is an extension of weinstein s theory or in energy terms the generalized fourier expansion of the lagrangian multiplier the merits of this method lie in the fact that the eigenvalues and eigenfunctions of structures are used as base structures the coupling of these structures are taken into account by lagrangian generalized forces of the constraint acting on the base structures some examples are given and the results compared with known solutions

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

on the solvability of the constrained lyapunov problem this paper considers system theoretic conditions for the solvability of the so called constrained lyapunov problem for nonsquare systems these problems commonly appear in the control systems literature both a static output feedback problem and an observer problem are considered the basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way

modalized observers the purpose of this paper is to present a special full order observer which utilizes a priori information concerning the initial condition mismatch in its design this a priori information and the use of an eigenstructure assignment procedure in the design leads to a reduction of the impact of the mismatch

difference equations of q appell polynomials in this paper we study some properties of the q appell polynomials including the recurrence relations and the q difference equations which extend some known classical q 1 results we also provide the recurrence relations and the q difference equations for q bernoulli polynomials q euler polynomials q genocchi polynomials and for q hermite polynomials as special cases of q appell polynomials

reducing the sensitivity to parameter variations of a minimum order reduced order observer a quantitative upper hound is established which defines the extent to which a minimum order reduced order non adaptive observer may be rendered insensitive to parameter variations that upper bound depends on the number of measurements and the location of questionable parameters within the system matrices an integral squared error objective function is explicitly solved that objective function may be used to assess the sensitivity of the system to parameter errors a numerical example is presented for a continuous observer the results are extended to the discrete ease

brief variable structure output feedback control design for a class of uncertain dynamic systems in this paper we consider the problem of designing a variable structure output feedback control vsofc law for a class of uncertain systems with mismatched uncertainty in the state matrix we derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities lmis and we give vsofc strategies we also give a simple design procedure and parameterizations of the linear switching surfaces together with solvability conditions for the given constrained lmis finally we give a design example in order to show the effectiveness of our method

a first order lyapunov robustness method for linear systems with uncertain parameters a method for stability robustness analysis based on a quadratic lyapunov function that varies linearly with uncertainty parameters is derived linear time invariant systems with structured uncertainties are discussed the lyapunov function is optimized numerically to maximize the robustness region in parameter space numerical results are given for four examples in which the first order method is compared to previous lyapunov methods for robustness analysis while the zero order method is slightly better than the first order method for one example the first order method is clearly superior in the other three more realistic examples the first order method is especially superior for applications to active control of flexible structures where robustness with respect to unmodeled coupling between modeled modes are important issues for such applications the first order method is much better at detecting the increased robustness associated with increased separation between frequencies

laguerre type exponentials and generalized appell polynomials general classes of two variables appell polynomials are introduced by exploiting properties of an iterated isomorphism related to the so called laguerre type exponentials further extensions to the multi index and multivariable cases are mentioned

disturbance attenuation for systems with input saturation an lmi approach a new design technique is proposed to improve disturbance attenuation for systems with input saturation the main results rely on a multiobjective approach which combines the quadratic stabilization technique with constraints on inputs for the full state feedback problem the sufficient conditions for the feasibility of a high gain controller are expressed in terms of linear matrix inequalities lmi for output feedback design the controllers are assumed to have an observer based structure the sufficient conditions for the output feedback controller to recover the full state properties are also given in terms of lmi

output feedback stabilization of uncertain dynamical systems given an uncertain dynamical system with a linear nominal part matched uncertainties and a measured output a sufficient condition is given for the existence of an output feedback stabilizing controller for the general multiinput multioutput case checking the sufficient condition involves the selection of a matrix f for the special class of single input single output systems f is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real then an output feedback stabilizing controller does indeed exist

robust stability and performance via fixed order dynamic compensation two robust control design problems are considered the robust stabilization problem in volves deterministically modeled bounded butunknown time varying parameter variations while the robust performance problem includes in addition a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations for both problems the design goal is a fixed order i e reduced or full order dynamic strictly proper feedback compensator a sufficient condition for solving the robust stabilization problem is given by means of a quadratic lyapunov function parameterized by the compensator gains for the robust performance problem the lyapunov function provides an upper bound for the closed loop performance this leads to consideration of the auxiliary minimization problem minimize the performance bound over the class of fixed order controllers subject to the lyapunovofunction constraint necessary conditions for optimality in the auxiliary problem thus serve as sufficient conditions for robust stability and performance in the original problem two particular bounds are considered for constructing the quadratic lyapunov function the first corresponds to a right shift multi plicative white noise model while the second was suggested by recent work of petersen and hollot the main result is an extended version ofthe optimal projection equations for fixed order dynamic compensation whose solutions are guaranteed to provide both robust stability and robust performance

generating functions via integral transforms abstract in this paper we use some integral transforms to derive for a polynomial sequence p n x n 0 generating functions of the type g x t n 0 n p n x t n starting from a generating function of type g x t n 0 p n x t n where n n 0 is a real numbers sequence independent on x and t that allows us to unify the treatment of a generating function problem for many well known polynomial sequences in the literature

modeling of parameter variations and asymptotic lqg synthesis conventional approaches in modern robustness and sensitivity theory are not adequate for the problems associated with parameter variation since the structure of parameter variations cannot be modeled properly or included in the synthesis procedure a new modeling technique is proposed to handle a class of structured plant uncertainties in a direct way the key is to treat deterministic parameter variations as an internal feedback loop so that the structure of parameter variations is embedded in its model an asymptotic lqg design synthesis based on this modeling method is also presented an important relationship between the structure of plant uncertainties and the lqg weighting matrices is obtained this relationship clearly specifies the kind of parameter variations allowable for the lqg ltr method

inverse structural modification using constraints in a structural modification problem the mass and stiffness matrices are modified to obtain a desired spectrum in this paper this is done by imposing constraints on the structure the undamped natural vibrations of a constrained linear structure are calculated by solving a generalized eigenvalue problem derived from the equations of motion for the constrained system involving lagrangian multipliers the coefficients of the constraint matrix are taken as design variables and a set of equations defining the inverse structural modification problem is formulated this modification problem requires an iterative method for its solution an algorithm based on newton s method is employed each iteration step involves the calculation of a rectangular jacobian and the solving of an associated underdetermined system of linear equations the system can be solved by using the moore penrose inverse the method is demonstrated in some numerical examples

output feedback control of uncertain coupled systems the stabilization of uncertain dynamical systems on n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively is studied we refer to the nc dimensional sybsystem as the reduced order system and to the nr dimensional subsystem as the residual system the overall n dimensional system is termed the full system the prototype for which is a mechanical model arising in the study of the active control of structures each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class the output available for feedback purposes is an nc valued linear combination of the state components of the full system and is subject to bounded measurement noise with known bound an output feedback strategy is described and sufficient conditions are obtained for the existence of a calculable global uniform compact attractor containing the state origin for controlled systems of this class

brief paper stability and h2 objective characterizations in control a comparative study this paper is concerned with stability and h 2 objective characterizations in control new forms of alternative lmi characterizations are presented for continuous time stability and h 2 objective a key relationship between the alternative characterizations for continuous time systems and the existing discrete time versions is illustrated the existing enhanced lmi characterization for continuous time systems called the reciprocal projection lemma is revisited and an alternative proof is provided with a new interpretation an e embedded lmi characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions through an application in control it is discussed that when applied to multi objective problems in control the alternative characterizations in this paper lead to an lmi solution with further significant conservativeness reduction compared to the reciprocal projection lemma in addition through the comparison with the existing dilated lmi condition it is shown that the dilated condition is an equivalent continuous time counterpart of the existing discrete time versions

h sub infinity optimal control as a weighted wiener hopf problem it is shown that h sub infinity optimization is equivalent to weighted h sub 2 optimization in the sense that the solution of the latter problem also solves the former the weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state space realization the authors do not suggest transforming h sub infinity optimization problems to h sub 2 optimization problems as a computational approach rather their results reveal an interesting connection between h sub infinity and h sub 2 optimization problems which is expected to offer additional insight for example h sub 2 optimal controllers are known to have an optimal observer full state feedback structure the result obtained shows that the minimum entropy solution of h sub infinity optimal control problems can be obtained as an h sub 2 optimal solution therefore it can be expected that the corresponding h sub infinity optimal controller has an optimal observer full state feedback structure

some results on quasi monomiality a polynomial set p n n 0 is called quasi monomial if and only if it is possible to define two operators p and m independent of n such thatp p n x np n 1 x andm p n x p n 1 x in this paper we show that every polynomial set is quasi monomial and we present some useful tools to explicitly express the p and m operators for some polynomial families given by their generating functions the obtained results are applied to boas buck polynomial sets

derivation of identities involving some special polynomials and numbers via generating functions with applications the current article focus on the ordinary bernoulli euler and genocchi numbers and polynomials it introduces a new approach to obtain identities involving these special polynomials and numbers via generating functions as an application of the new approach an easy proof for the main result in 6 is given relationships between the genocchi and the bernoulli polynomials and numbers are obtained some interesting identities are discovered

on linearization and connection coefficients for generalized hermite polynomials abstract we consider the problem of finding explicit formulas recurrence relations and sign properties for both connection and linearization coefficients for generalized hermite polynomials most of the computations are carried out by the computer algebra system maple using appropriate algorithms

design of observer based robust stabilizing controllers abstract this paper is concerned with the problem of designing stabilizing control laws for linear systems with time varying uncertainty since the entire state cannot be measured the controller must operate on some estimate of the state the approach used is to first obtain a linear robust controller based on the assumption that the complete state is available then an estimated state is generated via an observer and this estimate used in the implementation of the controller examples indicate that the use of an observer usually reduces the magnitude of the tolerable uncertainty the amount of this reduction depends on the choice made for the measured state variables

differential equations satisfied by the components with respect to the cyclic group of order n of some special functions let f be a complex function of the variable z admitting a laurent expansion in an annulus c with center in the origin for an arbitrary positive integer n ricci s theorem asserts that the function f can be written as the sum of n functions f n k k 0 1 n 1 defined byf n k z 1n l 0n 1exp 2i klnfzexp2i ln z c in this paper we present a technique which starting from a suitable differential equation satisfies by the function f provides a differential equation satisfied by the functions f n k some known special functions are treated for illustration

observer based robust controller design for a linear system with time varying perturbations abstract in this paper an observer based robust controller design problem for the linear uncertain system is considered where the uncertain system is subject to the norm bounded and the structured time varying uncertainties using the riccati approach full order and reduced order observers are obtained to reconstruct the unmeasurable states so that the robust stability of the uncertain system can be guaranteed with the state feedback control law

some properties of hermite based sheffer polynomials abstract in this paper the concepts and the formalism associated with monomiality principle and sheffer sequences are used to introduce family of hermite based sheffer polynomials some properties of hermite sheffer polynomials are considered further an operational formalism providing a correspondence between sheffer and hermite sheffer polynomials is developed furthermore this correspondence is used to derive several new identities and results for members of hermite sheffer family

differential equation of appell polynomials via the factorization method let pn x n 0 be a sequence of polynomials of degree n we define two sequences of differential operators n and n satisfying the following properties n pn x pn 1 x n pn x pn 1 x by constructing these two operators for appell polynomials we determine their differential equations via the factorization method introduced by infeld and hull rev mod phys 23 1951 21 the differential equations for both bernoulli and euler polynomials are given as special cases of the appell polynomials

equivalence between two solvability conditions for a static output feedback problem the paper is devoted to providing a proof for showing the equivalence of solvability conditions proposed in galimidi and barmish 1986 and gu 1990 for a static output feedback problem

orthogonality of some polynomial sets via quasi monomiality the lowering operator s and the raising operator t associated with a polynomial set p n n 0 are two operators which are independent of n and satisfy the relationships s p n x np n 1 x and t p n x p n 1 x n n 0 in this paper we use these operators to study the orthogonality of some polynomial sets more precisely we state sufficient conditions in terms of the s and t operators to ensure the orthogonality we also express explicitly by means of the s operator the linear functional for which the orthogonality holds true we obtain some well known results as particular cases of the results presented in this paper

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

the relation of the d orthogonal polynomials to the appell polynomials abstract we are dealing with the concept of d dimensional orthogonal abbreviated d orthogonal polynomials that is to say polynomials verifying one standard recurrence relation of order d 1 among the d orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials in particular we are concerned in the present paper with the solution of the following problem p find all polynomial sequences which are at the same time appell polynomials and d orthogonal the resulting polynomials are a natural extension of the hermite polynomials a sequence of these polynomials is obtained all the elements of its d 1 order recurrence are explicitly determined a generating function a d 1 order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given among such polynomials one singles out the d symmetrical ones definition 1 7 which are the d orthogonal polynomials analogous to the hermite classical ones when d 1 ordinary orthogonality we meet again the classical orthogonal polynomials of hermite

letter to the editor remarks on differential equation of appell polynomials we show that a recent result of he and ricci j comp appl math 139 2002 231 on differential equations for appell polynomials is valid for all polynomial sequences

on the stability robustness of the continuous time lqg optimal control the robustness properties of the lqg optimal controller that is obtained by the asymptotic recovery method are discussed it is shown that in spite of the good recovered stability margins the resulting closed loop design is inherently unrobust in the sense that small parameter variations in the plant and or small realization errors in the controller may lead to an instantaneous instability of the design

classes of hypercomplex polynomials of discrete variable based on the quasi monomiality principle with the aim of derive a quasi monomiality formulation in the context of discrete hypercomplex variables one will amalgamate through a clifford algebraic structure of signature 0 n the umbral calculus framework with lie algebraic symmetries the exponential generating function egf carrying the continuum dirac operator d j 1 n e j x j together with the lie algebraic representation of raising and lowering operators acting on the lattice h z n is used to derive the corresponding hypercomplex polynomials of discrete variable as appell sets with membership on the space clifford vector valued polynomials some particular examples concerning this construction such as the hypercomplex versions of falling factorials and the poisson charlier polynomials are introduced certain applications from the view of interpolation theory and integral transforms are also discussed

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

some discrete d orthogonal polynomial sets in this paper we characterize all polynomial sets which are at the same time d orthogonal and appell the resulting polynomials reduce to charlier polynomials for d 1 1 various properties of the obtained polynomials are singled out generating function recurrence relation of order d 1 and a difference equation of order d 1 we also explicitly express the d dimensional functional for which the d orthogonality holds