performance limitations of non minimum phase systems in the servomechanism problem abstract this paper studies the cheap regulator problem and the cheap servomechanism problem for systems which may be non minimum phase the study extends some well known properties of perfect regulation and the perfect tracking and disturbance rejection of minimum phase systems to non minimum phase systems it is shown that perfect rejection to disturbances applied to the plant input can be achieved no matter whether the system is minimum phase or non minimum phase whereas a fundamental limitation exists in the achievable transient performance of tracking and rejection to disturbances applied to the plant output for a non minimum phase system and that this limitation can be simply and completely characterized by the number and locations of those zeros of the system which lie in the right half of the complex plane furthermore this limitation provides a quantitative measure of the degree of difficulty which is inherent in the control of such non minimum phase systems

smoothness of equisingular families of curves francesco severi 1921 showed that equisingular families of plane nodal curves are t smooth i e smooth of the expected dimension whenever they are non empty for families with more complicated singularities this is no longer true given a divisor d on a smooth projective surface it thus makes sense to look for conditions which ensure that the family v irr d s 1 s r of irreducible curves in the linear system d l with precisely r singular points of types s 1 s r is t smooth considering different surfaces including the projective plane general surfaces in p 3 c products of curves and geometrically ruled surfaces we produce a sufficient condition of the type e t i 1 s i d k 2 where is some invariant of the singularity type and is some constant this generalises the results of greuel lossen and shustin 2001 for the plane case combining their methods and the method of bogomolov instability for many singularity types the invariant leads to essentially better conditions than the invariants used by greuel lossen and shustin 1997 and for most classes of geometrically ruled surfaces our results are the first known for t smoothness at all

h ltr procedure with specified degree of recovery this paper presents a new loop transfer recovery procedure which recovers a robustness property at plant inputs to a specified degree it is pointed out that generally the controller obtained by ltr method is stable a difference between the open loop transfer function of a state feedback system by lq regulator and that of an output feedback system by lq regulator with observer is estimated quantitatively by h norm a design problem of full minimal order observers for which the norm is less than a specified value is proposed this problem is reduced to an h optimal control problem with state feedback the design procedure is applicable to not only minimum phase plants but also non minimum phase plants the relation between this method and lqg ltr method is examined

loop transfer recovery for linear systems with delays in the state and the output this paper presents robustness properties of the kalman filter and the associated lqg ltr method for linear time invariant systems having delays in both the state and the output a circle condition relating to the return difference matrix associated with the kalman filter is derived using this circle condition it is shown that the kalman filter guarantees 1 2 gain margin and 60 phase margin which are the same as those for non delay systems however it is shown that even for minimum phase plants the lqg ltr method cannot recover the target loop transfer function instead an upper bound on the recovery error is obtained by using an upper bound of the solution of the kalman filter riccati equations finally some dual properties between output delayed systems and input delayed systems are exploited

linear quadratic gaussian synthesis with reduced parameter sensitivity we present a method for improving the tolerance of a conventional lqg controller to parameter errors in the plant model the improvement is achieved by introducing additional terms reflecting the structure of the parameter errors into the lqr cost function and also the process and measurement noise models adjusting the sizes of these additional terms permits a trade off between robustness and nominal performance manipulation of some of the additional terms leads to high gain controllers while other terms lead to low gain controllers conditions are developed under which the high gain approach asymptotically recovers the robustness of the corresponding full state feedback design and the low gain approach makes the closed loop poles asymptotically insensitive to parameter errors

a fuzzy flight controller combining linguistic and model based fuzzy control in this paper we address the design of a fuzzy flight controller that achieves stable and robust aggressive manoeuvrability for an unmanned helicopter the fuzzy flight controller proposed consists of a combination of a fuzzy gain scheduler and linguistic mamdani type controller the fuzzy gain scheduler is used for stable and robust altitude roll pitch and yaw control the linguistic controller is used to compute the inputs to the fuzzy gain scheduler i e desired values for roll pitch and yaw at given desired altitude and horizontal velocities the flight controller is obtained and tested in simulation using a realistic nonlinear mimo model of a real unmanned helicopter platform the apid mk

interpolation approach to h estimation and its interconnection to loop transfer recovery abstract this paper proposes to solve the h optimal estimation problem via interpolation theory the advantages of this approach are the following i direct and simple solutions can be obtained for the optimal estimators ii frequency weightings on estimation error and disturbance can be easily incorporated and iii unnecessary high observer gains can be avoided we also show the interconnection between the h optimal estimation problem and the optimal loop transfer recovery problem the interpolation approach applies to both continuous time and discrete time systems

sensitivity properties of a class of discrete time lqg controllers with computation delays sensitivity properties of the discrete time lqg controller which utilizes the optimal state predictor to compensate l step computation delays are discussed we obtain multiplicative decompositions of the sensitivity matrices at the input and output of a plant which clarify the effect of computation delays and imperfect observation furthermore these decompositions are used to show that duality between the sensitivity properties at the input and those at the output holds for l 1 and to identify the asymptotic sensitivity matrices obtained by loop transfer recovery procedures

on the noether lefschetz theorem and some remarks on codimension two cycles here of general moduli means that there is a countable union v of subvarieties of the space pn of surfaces of degree d in p3 such that the statement pie s z holds for s p n v noether it would seem stated this theorem but never completely proved it instead he gave a plausibility argument based on the following construction 1 let g be the hilbert scheme of curves of degree n and genus 9 in p3 l gr3 d l ip n the space of surfaces of degree d in p3 and zc t the incidence correspondence s o a c s c z s

characterizing nilpotent leibniz algebras by a new bound on their second homologies abstract let l be a finite dimensional nilpotent leibniz algebra such that dim l n and dim l 2 m 0 in this paper we prove dim h l 2 l n m 2 n m m 2 where h l 2 l is the second leibniz homology of l as a consequence for a non abelian nilpotent leibniz algebra l we find that s l n 1 2 1 dim h l 2 l 0 furthermore we determine all finite dimensional nilpotent leibniz algebras with s l less than or equal to three

deformation quantization of leibniz algebras abstract in this paper we use the local integration of a leibniz algebra h using a baker campbell hausdorff type formula in order to deformation quantize its linear dual h more precisely we define a natural rack product on the set of exponential functions on h which extends to a rack action on c h

adaptive output feedback design using asymptotic properties of lqg ltr controllers this technical note introduces an observer based adaptive output feedback tracking control design for multi input multi output dynamical systems with matched uncertainties the reported methodology exploits asymptotic behavior of lqg ltr regulators sufficient conditions for closed loop stability and uniform ultimate boundedness of the corresponding tracking error dynamics are formulated this method is valid for systems whose nominal linearized dynamics are controllable and observable we assume that the number of the system measured outputs sensors is greater than the number of the control inputs actuators and that the system output to input matrix product has full column rank in this case the system can be squared up i e augmented using pseudo control signals to yield relative degree one minimum phase dynamics since it is known that the squaring up problem is solvable for any controllable observable triplet a b c the proposed design is applicable to systems whose regulated output dynamics may be non minimum phase or have a high relative degree a simulation example is presented to demonstrate key design features

hnn extensions of leibniz algebras abstract in this paper we construct hnn extensions of diassociative algebras and leibniz algebras and prove that every leibniz algebra embeds into any of its hnn extensions we also prove that every leibniz algebra with at most countable dimension embeds into a two generator leibniz algebra

lqg ltr procedure using reduced order kalman filters abstractthis paper discusses a linear quadratic gaussian loop transfer recovery lqg ltr procedure using reduced order kalman filters by extending known exact recovery result the state space realisation commonly used for reduced order observer design is employed the zero structure intrinsic to the realisation is revealed asymptotic recovery is achieved using a non singular reduced order kalman filter with a parameterised set of covariance matrices the proposed procedure provides a systematic method for directly designing reduced order lqg controllers without additional coordinate transformations a numerical design example for a simple multivariable plant is presented to compare the proposed design with the standard lqg ltr design using a full order kalman filter

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

simultaneous recovery of loop transfer property and disturbance attenuation property by high gain observer the loop transfer property of a full state feedback control system can be recovered by an observer based controller provided the system is minimum phase and the observer gain is chosen appropriately it is possible that the closed loop transfer function from the disturbance to the controlled output cannot be recovered by the same observer as above even if the loop transfer function is recovered the disturbance attenuation property is shown to be recovered if the riccati equation that is to be solved in designing the observer is modified appropriately although the observer succeeds in recovering the disturbance attenuation property it may fail to recover the loop transfer property simultaneous recovery of both properties is therefore desirable in practical control system design it is shown that simultaneous recovery is possible if the number of independent measurement outputs is greater than or equal to the number of independent control and disturbance inputs the dual result is also given both p

some cohomologically rigid solvable leibniz algebras abstract in this paper we describe solvable leibniz algebras whose quotient algebra by one dimensional ideal is a lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical we prove that such leibniz algebra is unique and centerless also it is proved that the first and the second cohomology groups of the algebra with coefficients in the adjoint representation is trivial

solvable leibniz algebras with triangular nilradicals abstract in this paper the description of solvable lie algebras with triangular nilradicals is extended to leibniz algebras it is proven that the matrices of the left and the right operators on the elements of leibniz algebra have the upper triangular forms we establish that solvable leibniz algebra of a maximal possible dimension with a given triangular nilradical is a lie algebra furthermore solvable leibniz algebras with triangular nilradicals of the low dimensions are classified

cohomologically rigid solvable lie algebras with a nilradical of arbitrary characteristic sequence it is shown that for a finite dimensional solvable rigid lie algebra r its rank is upper bounded by the length of the characteristic sequence c n of its nilradical n for any characteristic sequence c n 1 n k 1 it is proved that there exists at least a solvable lie algebra re the nilradical of which has this characteristic sequence and that satisfies the conditions h p r c r c 0 for p 3

nodal curves on surfaces of general type plane irreducible curves of degree d having exactly nodes and no other singularities is non empty and everywhere smooth of codimension in the linear system o d if c vd severi uses the non speciality of the normal line bundle to the composition c c p where c is the normalization of c to prove that vd is smooth of the asserted codimension at the point c this proof can be extended to rational ruled and k3 surfaces with little changes we discuss this point in sect 1 see also t for the case of rational surfaces in the case of a surface of general type s the approach of severi fails and in fact it is easy to see that the analogous of severi s theorem does not hold in general if we impose too many nodes to the curves of a complete linear system d one may nevertheless look for an upper bound on ensuring that the family vd of irreducible curves in d with nodes is smooth of codimension in sect 2 we give the following partial answer to this problem

geometry of families of nodal curves on the blown up projective plane let p2r be the projective plane blown up at r generic points denote by e0 e1 er the strict transform of a generic straight line on p2 and the exceptional divisors of the blown up points on p2r respectively we consider the variety virr of all irreducible curves c with k nodes as the only singularities and give asymptotically nearly optimal sufficient conditions for its smoothness irreducibility and non emptiness moreover we extend our conditions for the smoothness and the irreducibility on families of reducible curves for r 9 we give the complete answer concerning the existence of nodal curves in virr

brief is set modeling of white noise a good tool for robust h2 analysis recently a new deterministic characterization of the h 2 norm has been proposed using a new norm w h based on approximate set membership modeling of white noise the main result shows that under mild conditions for a fixed system the gap between the h 2 and w h norms can be made arbitrarily small motivated by these results it has been argued that the w h norm provides a useful tool for analyzing robust h 2 controllers specially since in this context lmi based necessary and sufficient conditions for robust performance are available unfortunately as we show here with an example involving a very simple plant the worst case w h m norm can be conservative by at least a factor of m where m denotes the dimension of the exogenous signal for the original robust h 2 problem moreover the same example shows that competing state space based bounds also exhibit a similar degree of conservatism thus at this point the problem of finding non conservative bounds on the worst h 2 norm under lti or slowly varying ltv perturbations still remains open

leibniz algebras of heisenberg type we introduce and provide a classification theorem for the cl ass of heisenberg fock leibniz algebras this category of algebras is formed by those leibniz algebras l whose corresponding lie algebras are heisenberg algebras hn and whose hn modules i where i denotes the ideal generated by the squares of elements of l are isomorphic to fock modules we also consider the three dimensional heisenberg algebra h3 and study three classes of leibniz algebras with h3 as corresponding lie algebra by taking certain generalizations of the fock module moreover we describe the class of leibniz algebras with hn as corresponding lie algebra and such that the action i hn i gives rise to a minimal faithful representation of hn the classification of this family of leibniz algebras for the case of n 3 is given ams subject classifications 2010 17a32 17b30 17b10

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

solvable lie algebras with an mathbb n graded nilradical of maximal nilpotency degree and their invariants the class of solvable lie algebras with an graded nilradical of maximal nilpotency index is classified it is shown that such solvable extensions are unique up to isomorphism the generalized casimir invariants for the graded nilradicals and their associated solvable extensions are computed by the method of moving frames

plant directionality coupling and multivariable loop shaping we study the multivariable loop shaping problem when the plant is ill conditioned and feedback properties at both plant input and output are of interest directionality and coupling are described using the singular value decomposition and principal angles between high and low gain subspaces our first results are new first order approximations to feedback properties at one loop breaking point in terms of the open loop transfer function at that point secondly we study the relation between feedback properties at different loop breaking points in the event that the plant is ill conditioned the nominal relation is studied first then robustness is studied using a first order approximation to feedback properties at one point with respect to uncertainty at the other this analysis yields conditions that must be satisfied by feedback properties at one point to prevent poor feedback properties at the other finally these two sets of results are combined to show how feedback properties at both points may be

leibniz representations of lie algebras aleibniz representationof the lie algebra g is a vector spacemequipped with two actions left and right g m mand m g mwhich satisfy the relations formula when one of the variables is inmand the two others are in g in this paper we show that the categoryl g of finite dimensional leibniz representations of a finite dimensional semi simple lie algebra is not semi simple but thatl g has global dimension 2 we give an explicit description of the extensions of simple objects and we obtain the description of the quiver ofl g in the sense of gabriel it turns out thatl g is tame only for g sl2 we give the complete list of indecomposable objects in that case

about leibniz cohomology and deformations of lie algebras abstract we compare the second adjoint and trivial leibniz cohomology spaces of a lie algebra to the usual ones by a very elementary approach the comparison gives some conditions which are easy to verify for a given lie algebra for deciding whether it has more leibniz deformations than just the lie ones we also give the complete description of the leibniz and lie universal infinitesimal deformation of the 4 dimensional diamond lie algebra used in the wzw model and study the case of its 5 dimensional analogue by computing massey products

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

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

convex methods for robust h sub 2 analysis of continuous time systems treats the robust h sub 2 performance question of evaluating the rejection of continuous time white noise in the worst case over structured uncertainty in the system a frequency domain convex condition for robust h sub 2 analysis is presented with analogous properties as in the discrete time case in particular necessary and sufficient results are obtained introducing a continuous time version of the methodology of set descriptions of white noise in addition a state space test in terms of linear matrix inequalities is developed for the robust h sub 2 problem in the case of constant uncertainty scalings which apply to nonlinear or time varying uncertainty thus the problem is rendered finite dimensional in the same situation in which robust h sub spl infin analysis is finite dimensional

leibniz algebras with small derived ideal abstract a nilpotent leibniz algebra l is called extra special if dim z l dim l 2 1 in this paper the structure the second homology and the capability of extra special leibniz algebras are completely determined

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

on the properties of augmented open loop stable plants using lqg ltr control in this technical note are presented new properties on the application of the continuous and discrete time lqg ltr control methodology when an open loop stable process plant is augmented by integrators and a specific choice of design parameters is made it is shown that the target feedback loop transfer matrix is made equal to a diagonal transfer matrix of integrators with specifiable gains guaranteeing equal and decoupled responses in each of the system s outputs

characterization of zeros in two frequency scale systems we study the asymptotic behavior of the zeros of a two frequency scale transfer function in terms of the zeros of its slow and fast transfer functions by introducing the notion of type index we will show that all zeros of a two frequency scale transfer function with the type index of either spl nu spl ges 0 or spl nu 1 can be completely characterized in a manner that is quite similar to the characterization of the poles we also give a partial characterization for all other zeros in terms of the cardinality of their zero sets

on robust observer compensator design abstract this paper presents for the first time a unified explicit and restriction free set of design formulas for kalman type and luenberger type state observers and function observers with arbitrary poles in addition a new explicit and deterministic observer pole selection method for recovering the robustness of a direct state feedback system is also proposed two design examples are given in this paper these examples demonstrate the advantages of this robust recovery method the examples also show that both the luenberger type observers and the function observers generally have better stability margins this design methodology enables the design objectives of robustness order reduction and performance to be considered together in terms of observer pole selection

extended discrete time ltr synthesis of delayed control systems abstract this paper addresses compensation of dealys within a multi input multi output discrete time feedback loop for application to real time distributed control systems the delay compensation algorithm formulated in this paper is an extension of the standard loop transfer recovery ltr procedure from one step prediction to the general case of p step prediction p 1 it is shown that the steady state minimum variance filter gain is the h 2 minimization solution of the relative error between the target sensitivity matrix and the actual sensitivity matrix for p step prediction p 1 this concept forms the basis for synthesis of robust p step delay compensators p 1 the proposed control synthesis procedure for delay compensation is demonstrated via simulation of the flight control system of an advanced aircraft

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

an exact solution to continuous time mixed h sub 2 h sub spl infin control problems multiobjective control problems have been the object of much attention in the past few years since they allow for handling multiple perhaps conflicting performance specifications and model uncertainty one of the earliest multiobjective problems is the mixed h sub 2 h sub spl infin control problem which can be motivated as a nominal lqg optimal control problem subject to robust stability constraints this problem has proven to be surprisingly difficult to solve and at this time no closed form solutions are available moreover it has been shown that except in some trivial cases the optimal controller is infinite dimensional in this paper we propose a solution to general continuous time mixed h sub 2 h sub spl infin problems based upon constructing a family of approximating problems obtained by solving an equivalent discrete time problem each of these approximations can be solved efficiently and the resulting controllers converge strongly in the h sub 2 topology to the optimal solution

theory of ltr for non minimum phase systems recoverable target loops and recovery in a subspace part 1 analysis a complete analysis of loop transfer recovery problem using full order observer based controllers for general not necessarily left invertible and not necessarily minimum phase systems is considered the analysis here while showing that neither exact nor asymptotic loop transfer recovery is in general possible focuses on three fundamental issues the first issue is concerned with what can and what canot be achieved for a given system and for an arbitrarily specified target loop transfer function while the second issue is concerned with the development of necessary and or sufficient conditions a target loop has to satisfy so that it can be either exactly or asymptotically be recovered for a given system the third issue deals with the development of method s to test whether recovery is possible in a given subspace of the control space or not i e to test whether projections of target and achievable sensitivity and complimentary sensitivity functions onto a given subspace match each other or not such an

simplified rapid switching gain scheduling for a class of lpv systems a limitation of the original gain scheduling approaches is that the closed loop stability can only be assured when the underlying parameters vary sufficiently slowly a remedy exists but requires for its implementation the possible solution of asymptotic riccati equations are for an infinite number of different parameter values and the on line solution of a riccati differential equation rde with time varying coefficient matrices our method avoids solving the rde online and instead uses an explicit transient formula that looks up the predetermined solutions of the associated ares at a finite set of given system operating points furthermore only a finite number of ares are solved to determine a finite set of controller gains

invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements the invariants of solvable lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on cartan s method of moving frames

on the robustness of meop design versus asymptotic lqg synthesis an analysis is presented of generalized lqg linear quadratic gaussian type algorithms with regard to robustness characteristics comparisons are made of the maximum entropy optimal projection meop methodology versus the linear quadratic gaussian with loop transfer recovery lqg ltr technique and the parametric robust linear quadratic gaussian synthesis procedure the performance of a reduced order direct controller design is compared with the full order designs on a example representative of typical flexible structure dynamics

existence of curves with prescribed topological singularities throughout this paper we study the existence of irreducible curves c on smooth projective surfaces with singular points of prescribed topological types s 1 s r there are necessary conditions for the existence of the type r i 1 s i c 2 c k for some fixed divisor k on and suitable coefficients and and the main sufficient condition that we find is of the same type saying it is asymptotically proper ten years ago general results of this quality were not known even for the case e p 2 c an important ingredient for the proof is a vanishing theorem for invertible sheaves on the blown up e of the form o d r i 1 m i e i deduced from the kawamata vieweg vanishing theorem its proof covers the first part of the paper while the middle part is devoted to the existence theorems in the last part we investigate our conditions on ruled surfaces products of elliptic curves surfaces in p 3 c and k3 surfaces

extension of linear quadratic optimal control theory for mixed backgrounds the problem of finding an optimal controller while both deterministic and stochastic signals are present in the feedback system is addressed a general framework is developed to solve the above problem and to unify conventional frequency domain lq and lqg optimal control theories both the system transient and steady state behaviours are considered and the exact tracking of the arbitrary reference signal is guaranteed the decomposition of a mixed signal into the deterministic and stochastic parts gives a chance to investigate the effect of the weighting factors which were specified in the cost function on the compromise between transient and steady state system performance the solution which characterizes the structure of the optimal controller results in a set of independent diophantine equations instead of a set of coupled ones moreover the number of equations can be reduced under weak conditions finally both transient command tracking and steady state noise rejection capabilities can be op

reduced order dynamic compensator design for stability robustness of linear discrete time systems a reduced order dynamic compensator design is presented with stability robustness for linear discrete systems by including a stability robustness component in addition to the standard quadratic state and control terms in the performance criterion the robustness component is based on an unstructured perturbation stability bound for time varying perturbations the controller design is developed by the parameter optimization technique and involves the solution of five algebraic matrix equations four of which are discrete time lyapunov matrix equations

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given

robust nonlinear observer for lipschitz nonlinear systems subject to disturbances this note proposes a robust nonlinear observer for systems with lipschitz nonlinearity the proposed nonlinear observer whose linear part adopts the linear ltr observer design technique has two important advantages over previous designs first the new observer does not impose the small lipschitz constant condition on the system nonlinearity nor other structural conditions on the system dynamics as in the existing observer designs second it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances

some remarks on semisimple leibniz algebras abstract from levi s theorem it is known that every finite dimensional lie algebra over a field of characteristic zero is decomposed into semidirect sum of its solvable radical and semisimple subalgebra moreover semisimple part is the direct sum of simple ideals in barnes preprint 6 levi s theorem is extended to the case of leibniz algebras in the present paper we investigate the semisimple leibniz algebras and we show that the splitting theorem for semisimple leibniz algebras is not true moreover we consider some special classes of the semisimple leibniz algebras and we find a condition under which they decompose into direct sum of simple ideals

brief robust state predictive control with separation property a reduced state design for control systems with non equal time delays a robust state predictive control strategy is proposed for discrete time multi input output systems with non equal delays on signal buses it is based on a separation property between control and prediction the input delays are taken into account in the control law synthesis and the output delays are handled using an original steady state kalman predictor of order equal to the length of the state of the system without delays robustness especially against uncertain delays is improved using a state extension in the predictive gain synthesis the classic optimal separation theorem in the case of an one step predictor is extended to the general case of a d 1 step prediction for a delayed discrete time system

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

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

on dynamic output feedback compensator design using the riccati equation a simple formula for the design of dynamic output feedback compensators so as to reduce closed loop system sensitivity is given it is obtained by reformulating the compensator design problem as a deterministic linear optimal state regulator problem i e an lqg problem and an appropriate sensitivity reduction interpretation the result is given for siso linear systems

integral controller design based on disturbance cancellation partial ltr approach for non minimum phase plants for non minimum phase plants the loop transfer recovery ltr design of integral controllers based on the disturbance cancellation is considered since the design requires an unstabilizable extended plant the standard ltr method cannot be applied a new partial ltr method is proposed to overcome the difficulty the target of the proposed design is a fictitious controller including a disturbance estimator based on the measurement of the minimum phase state it is shown that the riccati equation including the gain matrix of the disturbance estimator in the target can be used to recover the target feedback property in the output feedback controller a simple design example is presented to show the effectiveness of the proposed method