direct data driven filter design for uncertain lti systems with bounded noise this paper investigates the filter design problem for linear time invariant dynamic systems when no mathematical model is available but a set of initial experiments can be performed where also the variable to be estimated is measured instead of using the initial experimental data to identify a model on the basis of which a filter is designed these data are used to directly design a filter assuming norm bounded disturbances and noises a set membership formulation is followed for classes of filters with exponentially decaying impulse response approximating sets are determined that guarantee to contain all the solutions to the optimal filtering problem where the aim is the minimization of the induced norm from disturbances to the estimation error a method is proposed for designing almost optimal linear filters with finite impulse response whose worst case filtering error is at most twice the lowest achievable one in the h siso case an efficient technique is presented that allows the evaluation of bounds on the guaranteed worst case filtering error of the designed filter numerical examples illustrate the effectiveness of the proposed solution

on preserving the robustness of an optimal control system with observers a new simple and general method is proposed in this note to preserve the robustness of the lq control system which involves state estimators the method is to minimize the estimator gain to the system input by selecting the estimator poles while the existing method is to maximize the estimator gain to the system output by introducing additional noise in the system input noise description an example demonstrates that the stability margin of the feedback system with the estimator designed by this method is even better than that of a system without the estimators

generalized ccr flows we introduce a new construction of e0 semigroups called generalized ccr flows with two kinds of descriptions those arising from sum systems and those arising from pairs of c0 semigroups we get a new necessary and sufficient condition for them to be of type iii when the associated sum system is of finite index using this criterion we construct examples of type iii e0 semigroups which can not be distinguished from e0 semigroups of type i by the invariants introduced by boris tsirelson finally by considering the local von neumann algebras and by associating a type iii factor to a given type iii e0 semigroup we show that there exist uncountably many type iii e0 semigroups in this family which are mutually non cocycle conjugate

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

dissipativity based resilient filtering of periodic markovian jump neural networks with quantized measurements the problem of dissipativity based resilient filtering for discrete time periodic markov jump neural networks in the presence of quantized measurements is investigated in this paper due to the limited capacities of network medium a logarithmic quantizer is applied to the underlying systems considering the fact that the filter is realized through a network randomly occurring parameter uncertainties of the filter are modeled by two mode dependent bernoulli processes by establishing the mode dependent periodic lyapunov function sufficient conditions are given to ensure the stability and dissipativity of the filtering error system the filter parameters are derived via solving a set of linear matrix inequalities the merits and validity of the proposed design techniques are verified by a simulation example

optimal l sub spl infin to l sub spl infin estimation for periodic systems in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l sub spl infin of the estimation error in the case of linear periodically time varying systems subjected to unknown but magnitude bounded l sub spl infin inputs these inputs consist of process and observation noises and the optimization problem is considered over an infinite time horizon lifting techniques are utilized to transform the problem to a time invariant l sub 1 model matching problem subject to additional constraints taking advantage of the particular structure of the estimation problem it is shown how standard methods of l sub 1 optimization in particular the delay augmentation technique can be suitably modified to solve this nonstandard problem

optimum performance levels for minimax filters predictors and smoothers abstract for both discrete and continuous time linear time varying systems we obtain the achievable performance levels for minimax filters predictors and smoothers in terms of the finite escape times of some related discrete and continuous time riccati equations our game theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in 1 they are all bayes estimators with respect to particular gaussian distributions and admit recursive structures

an lmi approach to periodic discrete time unbiased filtering the problem of unbiased filtering for a discrete time linear periodic system is faced by means of linear matrix inequality techniques as leading case we derive the synthesis conditions to obtain an unbiased filter and an unbiased fixed lag smoother enforcing a bound on the h performance on the error dynamics

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

pole assignment problem for discrete time linear periodic systems abstract this paper considers the pole assignment problem for discrete time linear periodic systems through the use of linear periodic state variable feedback control it is shown that if the n periodic system with m inputs and n states is completely reachable then the problem can be reduced to the pole assignment problem for a discrete time linear invariant system with nm inputs and n states

two dimensional solutions of a mean field equation on flat tori abstract we study the mean field equation on the flat torus t c z z u e u t e u 1 t 0 where is a real parameter for a general flat torus we obtain the existence of two dimensional solutions bifurcating from the trivial solution at each eigenvalue up to a multiplicative constant t of laplace operator on the torus in the space of even symmetric functions we further characterize the subset of all eigenvalues through which only one bifurcating curve passes finally local convexity near bifurcating points of the solution curves are obtained

scheduling of a limited communication channel for optimal control in this paper a method for optimal off line scheduling of a limited resource used for control purposes is presented for various reasons real time communication channels are prone to have limited bandwidth to overcome this obstacle the rate of actions must be chosen accordingly at design time both with respect to the limitation of the resource and to control performance a resulting off line schedule implements the rate of actions as a repetitive sequence of communication instants periodic control theory is used to define a cost functional for lq control that measures the performance of a sampled data system in relation to a desired continuous time performance in contrast to uniform sampling the communication sequence is here allowed to be time varying this approach results in a complex combinatorial optimization problem whose solution gives the optimal off line schedule i e the sequence in which the actions should take place the optimization problem is solved by a neighborhood search method where a heuristic method is used to generate initial guesses close to the optimum the optimal schedule is typically such that the sampling is non uniform but the resulting lq control law is time varying and takes this non uniform sampling into account

dead beat observers of reduced order for linear periodic discrete time systems with inaccessible inputs in this paper necessary and sufficient conditions are given for the existence of a dead beat observer for a linear periodic discrete time system subject to immeasurable periodic disturbances the conditions express in terms of the disturbed system the reconstructibility of the augmented system obtained by connecting the former with the disturbance generator a synthesis procedure of the observer is also provided

brief paper disturbance decoupling in fault detection of linear periodic systems this paper studies fault detection problems of linear discrete time periodic systems the aim is to design residual generators which deliver a residual signal fully decoupled from unknown disturbances first a periodic parity relation based full decoupling residual generator with a periodically varying parity vector is established then the relation between periodic parity vectors and periodic observer based residual generators is investigated it is shown that a periodic observer based full decoupling residual generator can be obtained from a periodic full decoupling parity vector finally the condition of disturbance decoupling is discussed and an example is given to illustrate the proposed approaches

every sum system is divisible we show that every sum system is divisible combined with b v r bhat and r srinivasan s result this shows that every product system arising from a sum system and every generalized ccr flow is either of type i or type iii a necessary and sufficient condition for such a product system to be of type i is obtained

time invariant representation of discrete periodic systems a large number of results from linear time invariant system theory can be extended to periodic systems provided an equivalent time invariant system can be found this paper presents a simple and numerically reliable procedure to achieve the same it is shown that using a stacked representation of periodic systems under system equivalence a minimal order generalized state space description can always be obtained

steady state kalman filtering with an h error bound abstract an estimator design problem is considered which involves both l 2 least squares and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 state estimation error criterion subject to a prespecified h constraint on the state estimation error the h estimation error 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 the l 2 state estimation error the principal result is a sufficient condition for characterizing fixed order i e full and reduced order estimators with bounded l 2 and h estimation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 state estimation result given in 2

fault detection of linear discrete time periodic systems in this note an approach to the design of optimal fault detection systems for linear discrete time periodic systems is proposed which leads to an optimized compromise between robustness to unknown disturbances and sensitivity to faults the needed computation mainly consists in solving a difference periodic riccati system the proposed approach is finally illustrated by a numerical example

fault detection for linear periodic systems using a geometric approach using the geometric approach a solution is given to the problem of detecting faults in linear periodic discrete time systems the solution consists on developing an unknown input observer the existing conditions are provided in terms of new geometric notion of outer observable subspace that is the dual notion of inner reachable subspace making use of the new notion a residual generator is developed such that the residual is made independent of unknown input disturbance and its output free response goes asymptotically to zero

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

the structure of solutions of a semilinear elliptic equation we give a complete classification of solutions of the elliptic equation u k x e 2u 0 in r n n 3 for some interesting cases of k

optimal and robust controllers for periodic and multirate systems the problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete time periodic systems the solution consists of solving an equivalent time invariant standard l sup 1 optimization problem subject to an additional constraint this constraint assures the causality of the resulting periodic controller by the duality theory the problem is shown to be equivalent to a linear programming problem which is no harder than the standard l sup 1 problem also it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems finally the results are applied to the problem of robust stabilization of periodic and multirate systems

output stabilization via pole placement of discrete time linear periodic systems the output stabilization problem for discrete time linear periodic systems is solved both the state feedback control law and the state predictor are based on a suitable time invariant state sampled reformulation associated with a periodic system preliminary concepts of periodic system theory are briefly recalled in particular the structural properties of a linear discrete time periodic system are properly related to those of a time invariant system associated with it by resorting to such a time invariant reformulation the output stabilization problem via pole placement is solved the stabilizing controller is constituted by a control law and an asymptotic state predictor both of which are shown to be periodic

minimal time minimal order deadbeat regulator with internal stability this paper is concerned with the output deadbeat finite settling time regulation with internal stability for linear discrete time multivariable systems the two cases are treated separately the one is the regulation by state feedback and the other is the regulation through function observers for both cases the basic solvability conditions the minimal settling time and the characterizations of the minimal time regulators are derived throughout the paper the well posedness condition plays a fundamental role a deterministic version of the so called separation theorem in lqg problem is derived namely the minimal time state feedback regulator combined with the minimal time minimal order function observer yields the overall minimal time minimal order regulator by output feedback

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

computational issues for linear periodic systems paradigms algorithms open problems linear periodic systems originate in various control fields involving periodic phenomena in the beginnings of algorithmic developments for periodic systems computational detours have been often employed to reduce the computational problems for periodic systems to those for standard systems well known techniques are the employment of lifted representations in discrete time or the use of periodic generators in continuous time new computational paradigms evolved later whose main ingredients are numerically reliable and efficient algorithms for manipulating matrix products without forming explicitly them reduction of large scale structured matrix pencils without building the underlying pencils computing with discrete time periodic system models with time varying state dimensions or solving periodic matrix differential equations using multiple shooting techniques the paper will give a succinct overview of all these new developments and will point out some of still existing open computational problems

regulator synthesis using c a b pairs the concept of a c a b pair of subspaces was introduced in an earlier paper by the author to study problems of compensator design here it is shown that the same concept plays a basic role in the theory of tracking and regulation from a few fundamental properties the main results of regulator theory are derived in a relatively simple and straightforward manner another new feature is that we are able to allow the presence of an unknown input thereby unifying the fields of tracking and regulation and disturbance decoupling all results are fully constructive and an example is given to illustrate the theory

minimum h sub infinity norm regulation of linear discrete time systems and its relation to linear quadratic discrete games a solution is derived to the h sub infinity optimization problem that arises in multivariable discrete time regulation when the controller has full access to the state vector the solution method is based on the close relations that exist between linear quadratic differential game theory and h sub infinity optimization the existing theory of discrete time quadratic games is readily applied in order to derive the solution to a finite time horizon version of the h sub infinity optimization problem the solution of the infinite time horizon h sub infinity optimization problem is obtained by formally taking the limit of the number of stages to infinity

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

robust estimation and filtering in the presence of bounded noise optimal algorithms for robust estimation and filtering are constructed the noise is considered a deterministic variable belonging to a set described by a norm previous results obtained for complete one to one and approximate information by m milanese and r tempo ibid vol 30 p 730 8 1985 are extended to partial and approximate information this information is considered useful in dealing with dynamic systems not completely identifiable and or with two different sources of noise such as process and measurement noise for different norms characterizing the noise optimal algorithms in a min max sense are shown in particular for hilbert norms a linear optimal algorithm is the well known minimum variance estimator for l sub infinity norm an optimal algorithm computable by linear programming is presented state estimation is formalized in the context of the general theory for stable systems an approximate state estimation is obtained by neglecting higher order powers an upper bound determining the approximation introduced is derived a numerical example illustrates the application of the theory

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

a perturbation problem for the shift semigroup abstract motivated by b tsirelson s construction of e 0 semigroups of type iii we investigate a c 0 semigroup acting on the space of square integrable functions of the half line whose difference from the shift semigroup is a hilbert schmidt operator we give a description of such semigroups in terms of analytic functions on the right half plane and construct several examples

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

optimal data scaling for principal component pursuit a lyapunov approach to convergence in principle component pursuit pcp the essential idea is to replace the original non convex optimization problem of the matrix rank and the count of non zero entries by a convex optimization problem of the nuclear and ell 1 norms in the pcp literature it is rigorously proved that the validity of this idea depends on the coherence of the uncontaminated data specifically the lower the coherence is the equivalence of the convex optimization problem to the original non convex one will hold by a larger probability although the coherence index is fixed for a given data set it is possible to adjust this index by introducing different scalings to the data the target of this work is thus to find the optimal scaling of the data such that the coherence index is minimized based on the analysis of the pcp problem structure a non convex optimization problem with implicit dependence on the scaling parameters is firstly formulated to solve this problem a coordinate descent algorithm is proposed under mild conditions on the structure of the data matrix the convergence of the algorithm to a global optimal point is rigorously proved by treating the algorithm as a discrete time dynamic system and utilizing a lyapunov type approach monte carlo simulation experiments are performed to verify the effectiveness of the developed results

on the structure of the conformal gaussian curvature equation on r2 ii in this paper we continue our investigation initiated in ecn on the structure of the set of all possible solutions of the equation 1 1 au ke2 o in r 2 where a is the laplace operator and k is a given nonpositive locally hslder continuous function in r 2 equation 1 1 arises in the problem of finding a riemannian metric which realizes the given function k as its gaussian curvature and is conformal to the standard euclidean metric in r 2 we refer the reader to cn for a brief description of the background and the history of this problem the study of the equation 1 1 dates back to at least 1930 s but it seems that a complete classification of all solutions of 1 1 was obtained only very recently in cn for the case k x ix t near oo where l 2 is a constant here we continue to use the notation g near to denote that there exist two positive constants cl c2 such that c l f g c2f near oo as we did in cn more precisely the following result was established in cn theorem suppose that k 2 then the following conclusions hold i for each 0 1 1 possesses a unique solution u such that

on the stabilization of a class of bilinear systems abstract in this paper the problem of the stabilization of a class of continuous time bilinear systems containing the class of the homogeneous ones is studied and simple stabiliza bility conditions are derived expressed in terms of the stability or stabilizability of some linear or homogeneous bilinear subsystems of the given system on this basis it is shown that this problem can be decomposed into subproblems and reduced to the stabilization of homogeneous subsystems of the system obtained through successive decompositions of it a sufficient condition for the stabilization of a homogeneous bilinear system is also given

structure and optimality of multivariable periodic controllers a linear periodic plant to be controlled by measurement feedback is considered the general optimal synthesis problem in which the objective is to select a compensator to minimize the norm of the induced map between the controlled output and the exogeneous input is analyzed it is shown that the performance of any linear compensator possibly time varying nonperiodic can be matched by a compensator contained in the restricted class of periodic controllers this result is established in the discrete time case for bounded amplitude l sub infinity signals in the continuous time case the result is shown for bounded energy signals l sub 2 l sub 2

a lifting based approach to observer based fault detection of linear periodic systems in this note an approach based on lifting is introduced for the observer based fault detection fd of linear discrete time periodic systems the main contribution of this note is to give an analytic expression to transform the linear time invariant lti observer based residual generator designed based on the lifted lti reformulation of the periodic system into a periodic observer based residual generator to reduce detection delay the result enables a systematic transfer of the existing observer based fd methods for discrete lti systems to discrete time periodic systems

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

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

the conformal plate buckling equation the linear equation 2 u 1 for the infinitesimal buckling under uniform unit load of a thin elastic plate over r 2 has the particularly interesting nonlinear generalization g 2 u 1 where ag e 2u is the laplace beltrami operator for the metric g e 2u g 0 with g 0 the standard euclidean metric on r 2 this conformal elliptic pde of fourth order is equivalent to the nonlinear system of elliptic pdes of second order u x k g x exp 2u x 0 and k g x exp 2u x 0 with x r 2 describing a conformally flat surface with a gauss curvature function k g that is generated self consistently through the metric s conformal factor we study this conformal plate buckling equation under the hypotheses of finite integral curvature f kg exp 2u dx k finite area exp 2u dx a and the mild compactness condition k l 1 b 1 y uniformly with respect to y r 2 we show that asymptotically for x all solutions behave like u x 2 ln x c o 1 and k x 2 ln x c o 1 with 2 4 and 2 4 we also show that for each k 2 4 there exists a k and a radially symmetric solution pair u k satisfying k u k and max k k which is unique modulo translation of the origin and scaling of x coupled with a translation of u

periodic solutions of periodic riccati equations for periodically time varying matrix riccati equations controllability and observability in the usual sense are shown to be sufficient for the existence of a unique positive definite periodic solution

on optimal e to e filtering abstract in this paper we consider the problem of finding a filter that minimizes the worst case magnitude l of the estimation error in the case of linear time invariant systems subjected to unknown but magnitude bounded l inputs these inputs consist of process and observation noise as well as initial conditions also the optimization problem is considered over an infinite time horizon taking a model matching approach suboptimal solutions are presented that stem from the resulting l induced norm minimization problem

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

a canonical decomposition of linear periodic discrete time systems in this paper a linear periodic discrete time system is studied on the basis of simple properties of the subspaces of controllable states and of unreconstructible ones a canonical structure theorem is derived this generalizes 1o such a system the classical kalman decomposition while preserving the constant dimensionality of the four subsystems which arise when a periodic continuous time system is decomposed the dynamic matrices of the non controllable and or non reconstructible subsystems are shown to be non singular at each time instant as those for a time invariant discrete time system are

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

on the conformal gaussian curvature equation inr2 abstract in this paper we consider the equation u k x e 2u 0 in r 2 0 1 wherek x k x inr2andk x does not decay at x large from the geometric viewpoint it is quite interesting to ask what the best possible range is of total curvature of all solutions of 0 1 in this paper we study this problem for radial solutions we also construct some particularkto demonstrate the rich phenomenon in particular we show by examples that whenk x is negative for x large eq 0 1 possess a branch of solutions which satisfies some monotonicity property

strong stabilization with infinite multivariable gain margin through linear periodic control the problem of the strong stabilization with infinite gain margin with the additional requirement of a prescribed rate of convergence of the free responses is addressed for linear time invariant discrete time multivariable plants in the case when unknown different scalar gains act either on the inputs or on the outputs necessary and sufficient conditions for the solvability of the problem by means of a stable linear periodic discrete time output feedback dynamic controller are derived algorithmic procedures are given for designing the proposed periodic controllers