new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

technical communique a note on the robustness of high gain observer based controllers to unmodeled actuator and sensor dynamics it is shown that a nonlinear output feedback stabilizing controller which combines a globally bounded state feedback controller with a high gain observer is robust with respect to unmodeled fast actuator and sensor dynamics the actuator and sensor dynamics need to be sufficiently fast relative to the dynamics of the nominal closed loop system under state feedback but they need not be faster than the observer dynamics

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

robust stabilization relative to the unweighted h norm is generically unattainable in the presence of singular plant perturbations recent work by vidyasagar gives a sufficient condition under which a singularly perturbed system can be robustly stabilized relative to the unweighted h infty norm in this note we show that the same condition is also necessary in addition we prove that this condition is generically untrue with respect to the class of all linear singularly perturbed systems as well as the class of all singular perturbations of any fixed stabilizable and detectable system

robustness of dynamic output feedback control for singular perturbation systems abstract the problem of the robustness of dynamic output feedback control for singular perturbation systems is investigated the solution to this problem is reduced to the simultaneous design of static output feedback controllers for the fast subsystem and the so called auxiliary system of the slow subsystem some conditions are proposed to ensure the robustness of the actual closed loop system the exact upper bound of the parasitic parameter for the controlled system is also determined finally an actual model which failed in dynamic output feedback control in 4 is reexamined successfully here

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

robust stabilization of singularly perturbed systems abstract we discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models in 1 it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the true system containing both fast and slow modes this phenomenon was then expanded to include the case where the simplified system is strictly proper in 2 the objectives of this note are threefold i to show that given any proper system and any stabilizing controller for it that is proper but not strictly proper there exists a singular perturbation of the system that is destabilized by that controller ii to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter and iii to provide a characterization in the same spirit as 3 4 of the set of all strictly proper controllers that stabilize a given proper plant by combining these results it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system

a sampled data control scheme for stabilization of systems with unmodeled high frequency dynamics the output feedback stabilization problem is considered for linear sampled data control systems in the presence of unmodeled high frequency dynamics sufficient conditions for stabilization of such systems were given by m vidyasagar 1985 for strictly proper systems this paper extends the class of systems in order to include the proper systems case and proposes a conceptually novel digital control scheme in this scheme the control law based on the reduced order system is applied to the full system only during a short fraction of the sampling period during the second part of the sampling period the control is taken equal to zero such that without control the neglected fast states have sufficient time to converge to their equilibrium point

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

strict feedforward control systems linearisability and convergent normal forms this article discusses the feedback equivalence of multi inputs feedforward control systems via smooth resp analytic feedback transformations we first address the state resp feedback linearisation problem and provide easily computable algorithms that yield explicit state resp feedback linearising coordinates for systems in strict feedforward form the application of the algorithms does not require checking the commutativity resp involutivity of the distributions associated with the system and the algorithms fail after few steps if the system is not linearisable in the latter case the algorithms are extended to provide coordinate systems bringing the system into a normal form which is a smooth resp analytic counterpart of kang s formal normal form illustrative examples for both the linearisation and convergent normal form include the vertical take off and landing aircraft the multi vehicle wireless testbed among others

on the cohen strongly p summing multilinear operators abstract in this paper we introduce and study a new concept of summability in the category of multilinear operators which is the cohen strongly p summing multilinear operators we prove a natural analog of the pietsch domination theorem and we compare the notion of p dominated multilinear operators with this class by generalizing a theorem of bu cohen

a further note on the robustness of output feedback control methods to modeling errors in an earlier note it was shown that designing a nonstrictly proper output feedback compensator using a model that neglects parasitic elements might lead to an unstable closed loop system even when the neglected modes are asymptotically stable the purpose of this note is to show that this instability phenomenon might take place even when the reduced order design model is strictly proper

gain margin improvement using generalized sampled data hold function based multirate output compensator abstract for a siso strictly proper nonminimum phase continuous time linear time invariant lti plant it was shown in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr that the closed loop gain margin obtained via a generalized sampled data hold function gshf based dynamic compensator is significantly improved over that achieved via a conventional periodic controller used in francis b a and t t georgiou 1988 ieee trans automat contr ac 33 820 832 nevertheless the compensator so designed is not necessarily strictly proper it is well known that it is practically difficult and sometimes impossible to implement a nonstrictly proper compensator due to the requirement of zero computation time further as has been shown in vidyasagar m 1985 systems and control letters 5 413 418 stabilization by a nonstrictly proper controller is never robust against singular perturbations in this paper we propose a new type of gshf based compensator which employs multirate sampling of the plant output using the proposed compensator not only the same level of gain margin as in yan w b d o anderson and r r bitmead 1993 ieee trans automat contr can be achieved but also more importantly the compensator is strictly proper

a new stable compensator design for exact and approximate loop transfer recovery abstract in this paper a new compensator structure for loop transfer recovery ltr is proposed the proposed compensator a is open loop stable b guarantees closed loop stability and above all c requires much smaller values of gain than the conventional observer based controller for the same degree of loop transfer recovery the fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages the most important among them being the reduction in controller band width and freedom from the woes of saturation the trade off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly both full and reduced order compensators for ltr when the design specifications are reflected either at the input or at the output point of the given plant are considered numerical examples illustrate the advantages of the new compensator structure the new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used to motivate and deduce our new compensator structure a unified treatment of observer theory for ltr is presented in the context of such a unification some new results are also given

near optimal output feedback regulation of ill conditioned linear systems a two time scale approximation for the linear quadratic optimal output feedback regulator program is examined necessary conditions for optimality as well as an algorithm for computing locally near optimal gains are derived if it is assumed that the slow and fast subsystem initial conditions are uniformly distributed optimal gains for the two time scale problem provide a second order approximation to optimal closed loop performance in the unperturbed system this is verified with a numerical example

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

multiple summing operators on banach spaces abstract in this paper we improve some previous results about multiple p summing multilinear operators by showing that every multilinear form from l 1 spaces is multiple p summing for 1 p 2 the proof is based on the existence of a predual for the banach space of multiple p summing multilinear forms we also show the failure of the inclusion theorem in this class of operators and improve some results of y melendez and a tonge about dominated multilinear operators

strongly p summing multilinear operators abstract we define the concept of strongly p summing multilinear operators and prove that they have properly defined aron berner extensions some properties and examples are shown

on the gain margin improvement using dynamic compensation based on generalized sampled data hold functions this paper shows that the use of dynamic compensation based on generalized sampled data hold functions gshf can arbitrarily improve the gain margin for continuous time nonminimum phase linear systems the gshf compensator is a particular periodic digital controller the effect of sampling period on the gain margin is analyzed furthermore it is proved that under a mild condition the gain margin improvement can be achieved without forcing the sampling period small an important advantage of periodic compensation over lti compensation is found to be the capability of reducing conflict between gain margin and sensitivity

brief robust output feedback control of nonlinear singularly perturbed systems in this work we consider nonlinear singularly perturbed systems with time varying uncertain variables for which the fast subsystem is asymptotically stable and the slow subsystem is input output linearizable and possesses input to state stable iss inverse dynamics for these systems we synthesize a robust output feedback controller that ensures boundedness of the state and enforces robust asymptotic output tracking with attenuation of the effect of the uncertain variables on the output of the closed loop system the controller is constructed through combination of a high gain observer with a robust state feedback controller synthesized via lyapunov s direct method the proposed controller enforces the aforementioned properties in the closed loop system for initial conditions uncertainty and rate of change of uncertainty in arbitrarily large compact sets provided that the singular perturbation parameter is sufficiently small and the observer gain is sufficiently large

a tensor norm preserving unconditionality for lp spaces we show that for each n n there is an n tensor norm a in the sense of grothendieck with the surprising property that the tensor product y 1 y n has local unconditional structure for each choice of n arbitrary cp j spaces yj in fact a is the tensor norm associated to the ideal of multiple 1 summing n linear forms on banach spaces

a pseudospectral method for the optimal control of constrained feedback linearizable systems we consider the optimal control of feedback linearizable dynamical systems subject to mixed state and control constraints in general a linearizing feedback control does not minimize the cost function such problems arise frequently in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls in this paper we consider a pseudospectral ps method to compute optimal controls we prove that a sequence of solutions to the ps discretized constrained problem converges to the optimal solution of the continuous time optimal control problem under mild and numerically verifiable conditions the spectral coefficients of the state trajectories provide a practical method to verify the convergence of the computed solution the proposed ideas are illustrated by several numerical examples

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

on decomposition of nonlinear control systems in this paper the problem is studied when the system x i k 1 u t g t x x 0 x 0 defined on an n dimensional analytic manifold can be decomposed into either independent subsystems or a cascade of subsystems necessary and sufficient conditions for the existence of such local decompositions are given in terms of lie algebras generated by the system

output feedback control of linear two time scale systems output feedback control of linear time invariant singularly perturbed systems is studied the set of all compensators that stabilize a singularly perturbed system while preserving its two time scale structure is parameterized the parameterization is used to show that any two frequency scale stabilizing compensator can be asymptotically approximated by a compensator designed via a sequential procedure in this procedure a fast high frequency compensator is designed first to stabilize the fast model of the system then a strictly proper slow low frequency compensator is designed to stabilize a modified slow model the parallel connection of the two compensators forms a two frequency scale stabilizing compensator for the singularly perturbed system

on output feedback control of singularly perturbed systems we treat the problem of robustness of output feedback controllers with respect to singular perturbations given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a possibly dynamical output feedback controller we present a sufficient condition which ensures that the system obtained by applying the same controller to the original full order singularly perturbed control system is exponentially stable for sufficiently small values of the perturbation parameter this condition which is less restrictive than those previously given in the literature is shown to be always satisfied when the singular perturbation is due to the presence of fast actuators and or sensors furthermore we show explicitly that in the linear time invariant case if this condition is not satisfied then there exists an output feedback controller which stabilizes the reduced order system but destabilizes the full order system

controller reduction via stable factorization and balancing abstract a controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper for a certain right coprime factorization of an lqg designed controller k s n s d 1 s we approximate using a balancing technique the pair d s n s t by a low order pair d1 s n1 s t defining a factorization of the reduced order controller k 1 s n1 s d1 1 s we show that reducing the controller order in this way is motivated in a natural way which leads to the expectation of both good stability properties and good accuracy of approximation of closed loop behaviour this is also demonstrated in some examples

on the robustness of sampled data control to unmodeled high frequency dynamics robustness of sampled data control designs to unmodeled high frequency dynamics is studied using singular perturbation theory it is argued that when the plant is preceded by a zero order hold a direct transmission term of the reduced order model which results from neglecting high frequency dynamics should be modeled as a delay element in order to ensure robustness

input output decoupling of hamiltonian systems the linear case in this note we give necessary and sufficient conditions for a linear hamiltonian system to be input output decouplable by hamiltonian feedback i e feedback that preserves the hamiltonian structure in a second paper we treat the same problem for nonlinear hamiltonian systems

feedback linearizable feedforward systems a special class the problem of feedback linearizability of systems in feedforward form is addressed and an algorithm providing explicit coordinates change and feedback given at each step the algorithm replaces the involutive conditions of feedback linearization by some easily checkable we also reconsider type ii subclass of linearizable strict feedforward systems introduced by krstic and we show that it constitutes the only linearizable among the class of quasilinear strict feedforward systems our results allow an easy computation of the linearizing coordinates and thus provide a stabilizing feedback controller for the original system among others we illustrate by few examples including the vtol

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

the recursive algorithm for the optimal static output feedback control problem of linear singularity perturbed systems a recursive algorithm is developed for solving the algebraic equations comprising the solution of the optimal static output feedback control problem of singularly perturbed linear systems the algorithm is very efficient from the numerical point of view since only low order systems are involved in algebraic calculations and the required solution can be easily obtained up to an arbitrary order of accuracy that is o epsilon sup k where epsilon is a small perturbation parameter the real world example demonstrates the failure of o epsilon theory used so far in the study of this problem and the necessity for the existence of o epsilon sup k theory

a new approach to robust guaranteed cost control for uncertain multimodeling systems the guaranteed cost control problem for multimodeling systems with norm bounded uncertainty is investigated the main contribution in this paper is that a new independent controller is derived by solving the reduced order slow and fast algebraic riccati equations ares whose dimension is smaller than the dimension of full order multiparameter algebraic riccati equation mare it is shown that if these ares have a positive definite stabilizing solution then the closed loop system is quadratically stable and has the cost bound

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

on the stability of multiple time scale systems the stability of time invariant multiparameter singular perturbation problems is considered and the implications of two time scale stability results for multiple time scale systems are clarified an example shows that the asymptotic stability of a multiparameter singular perturbation problem under the bounded mutual ratios assumption for arbitrary bounds on the ratios of the small parameters does not imply asymptotic stability under the multiple time scales assumption for any ordering of the smallness of the parameters however this conclusion does apply when only two small parameters are present and the fast variables are scalar valued a multiparameter singularly perturbed system may be asymptotically stable for all sufficiently small and positive values of the perturbation parameters even though the boundary layer system does not satisfy the d stability criterion these examples are discussed in the light of the strong d stability condition which must be imposed to obtain results that are robus

bohr s strip for vector valued dirichlet series bohr showed that the width of the strip in the complex plane on which a given dirichlet series sum a n n s s in mathbb c converges uniformly but not absolutely is at most 1 2 and bohnenblust hille that this bound in general is optimal we prove that for a given infinite dimensional banach space y the width of bohr s strip for a dirichlet series with coefficients an in y is bounded by 1 1 cot y where cot y denotes the optimal cotype of y this estimate even turns out to be optimal and hence leads to a new characterization of cotype in terms of vector valued dirichlet series

on the exponential stability of singularly perturbed systems this paper establishes some results and properties related to the exponential stability of general dynamical systems and in particular singularly perturbed systems for singularly perturbed systems it is shown that if both the reduced order system and the boundary layer system are exponentially stable then provided that some further regularity conditions are satisfied the full order system is exponentially stable for sufficiently small values of the perturbation parameter mu and its rate of convergence approaches that of the reduced order system mu 0 as mu approaches zero exponentially decaying norm bounds are given for the slow and fast components of the full order system trajectories to achieve this result a new converse lyapunov result for exponentially stable systems is presented

quotient submanifolds for static feedback linearization a procedure for finding locally the linearizing output of a single input nonlinear affine system is proposed it relies on successive integrations of one dimensional distributions and projections along these submanifolds the algorithm proceeds recursively reducing the dimension one by one of both the number of coordinates and the number of vector fields until the solution is obtained a variant of the algorithm is also proposed which does not require the computation of the full initial distribution the proof of convergence of this second algorithm shows the importance of a new anti symmetrical product besides providing a new insight into the involutivity condition the algorithm can lead to a simple way of integrating the system of partial differential equations defining the linearizing output

technical communique on the klimushchev krasovskii theorem the klimushchev krasovskii theorem describes a sufficient condition for the asymptotic stability of singularly perturbed systems motivated by some subtle examples this note presents a new necessary and sufficient condition by imposing an additional assumption on the statement of the klimushchev krasovskii theorem this note also extends the main inertia theorem to singularly perturbed systems

frequency domain results for systems with slow and fast dynamics the mathematical treatment of systems with slow and fast dynamics has traditionally involved singular perturbation theory for differential equations this paper suggests a set of conditions to be placed on a frequency domain description of a system to guarantee two time scale behavior some basic stability and approximation results are presented

a geometric characterization of feedforward forms this note addresses the problem of local coordinates and feedback equivalence of single input affine nonlinear systems to feedforward forms in particular using the notions of invariant and controlled invariant distributions we provide necessary and sufficient conditions for a general affine in control nonlinear system to be locally coordinates or feedback equivalent to a system in strict feedforward form for illustration the general theory is applied to a simple four dimensional system describing the dynamics of a food chain

linearization of control systems we address the problem of static state linearization of multi input nonlinear control systems via coordinate transformation necessary and sufficient geometric conditions in terms of certain set of vector fields associated with the system were obtained in the early eighties stating the fact that such set of vector fields should be commutative and of constant rank the state linearization problem i e the finding of linearizing coordinates was thus reduced to solving a set of partial differential equations the objective of this paper is to provide an algorithm allowing to compute explicitly the linearizing state coordinates the algorithm is performed using a maximum of n 1 steps n being the dimension of the system and is made possible by extending the explicit solvability of the flow box theorem to a commutative set of vector fields examples are provided to illustrate the results an extension of the method to dynamic feedback linearization is also outlined

robust stabilization for composite observer based control of discrete systems abstract design criteria of robust observer based controllers for linear discrete time singularly perturbed systems with slow and fast modes are considered the developed stability measure complements the quantitative information for unmodeled fast modes that cannot be provided by the usual qualitative robustness analyses a numerical example is provided to show the analytical results obtained

paper optimal output feedback design of systems with ill conditioned dynamics singular perturbation concepts are exploited to develop a procedure for designing a constant gain output feedback control system it is assumed that the original system is ill conditioned in the sense that the plant contains widely separated dynamics and that an accurate description for the high frequency behavior may not be available the design procedure attempts to stabilize the system by minimizing a quadratic cost function made up of the control and states associated with a reduced order low frequency model for the plant and a measure of stability for the neglected fast dynamics the resulting design procedure does not require knowledge of the fast dynamics

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

state and feedback linearizations of single input control systems abstract in this paper we address the problem of state resp feedback linearization of nonlinear single input control systems using state resp feedback coordinate transformations although necessary and sufficient geometric conditions have been provided in the early eighties the problems of finding the state resp feedback linearizing coordinates are subject to solving systems of partial differential equations we will provide here a solution to the two problems by defining algorithms allowing to compute explicitly the linearizing state resp feedback coordinates for any nonlinear control system that is indeed linearizable resp feedback linearizable each algorithm is performed using a maximum of n 1 steps n being the dimension of the system and they are made possible by explicitly solving the flow box or straightening theorem we illustrate with several examples borrowed from the literature

composite fuzzy control of nonlinear singularly perturbed systems this paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed nsp systems with guaranteed hinfin control performance we use the takagi sugeno t s fuzzy model to construct the singularly perturbed fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained at first a set of common positive define matrices and the controller gains are determined by the lyapunov stability theorem and linear matrix inequality lmi approach then a sufficient condition is derived for the robust stabilization of nsp systems the composite fuzzy control will stabilize the original nsp systems for all epsivisin 0 epsiv and the allowable perturbation bound epsiv can be determined via some algebra inequalities a practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme

linear compensator designs based exclusively on input output information are never robust with respect to unmodeled dynamics the effects of unmodeled higher order dynamics or parasitics on the stability of linear control systems are investigated a description is first given of a class of perturbations of a given state equation that cannot be distinguished from the original on the basis of input output measurements alone then it is shown that given any plant compensator pair perturbations of each system of this type can always be found that destabilize the closed loop configuration the effect of destabilizing perturbations on output behavior is explored

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

w stability of feedback systems abstract this paper introduces the notion of w stability of feedback systems this is a generalization of a concept of well posedness discussed by willems w stability requires that a feedback system should remain stable under a certain class of perturbations which may not be vanishingly small when measured by the gap metric the paper derives necessary and sufficient conditions for a feedback system to be w stable further an investigation of well posedness is given for feedback systems where high frequency roll off has been suppressed for modelling simplicity this question is pertinent in standard pid control

singular perturbation analysis of high frequency filter design the control design of systems with lightly damped high frequency oscillatory modes is treated systems exhibiting these lightly damped modes include turbine generators and large flexible structures frequently the dynamics of these high frequency modes are not known very accurately as a result the design objective is to improve the slow dynamics without destabilizing the high frequency modes from a classical frequency domain design viewpoint this is in part a filtering problem requiring some kind of high frequency filter the singular perturbation method is used to systematically develop a two time scale method to design these high frequency filters and provides guidelines on the kind of high frequency filter to be used in addition the method provides an asymptotic error analysis the design is illustrated with an example representative of a power system model with a two mass turbine generator model

toward a theory of robust compensation for systems with unknown parasitics the problem of designing a robust compensator based on a plant model with order uncertainty is considered the uncertainty is characterized mathematically as a class of generalized singular perturbations of the plant the case of static compensation is examined a necessary and sufficient condition is established under which actual closed loop behavior is close to that predicted by the plant model under sufficiently small singular perturbations the condition is shown to be generic

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

l2 l synchronization for singularly perturbed complex networks with semi markov jump topology abstract this paper is concerned with the problem of l 2 l synchronization for singularly perturbed complex networks spcns with semi markov jump topology in which the phenomenon of the singular perturbation is fully taken into consideration the topology of complex dynamical network is time varying switching regulated by the semi markov jump mechanism the priority of this work is to obtain some conditions which ensure the underlying complex dynamical network cdn is stochastically synchronized with a stated l 2 l performance level based on lyapunov method and convex optimization technique the synchronization conditions can be obtained via solving convex optimization problems finally the correctness and validity of our proposed synchronization method are well demonstrated by a simulation example

robustness of linear feedback control systems to unmodelled high frequency dynamics a basic issue in the control of linear time invariant plants is the effect of neglected high frequency dynamics on the performance in particular on the closed loop stability of the control system in this paper the robustness of various output feedback control designs based on a reduced order model with neglected high frequency dynamics is investigated using singular perturbation techniques a general robust design rule is to avoid static output feedback for systems with unmodelled high frequency dynamics from a frequency domain standpoint the robust design rule is to avoid closing high frequency plant loops by using strictly proper controllers or controllers with a low pass filtering property

multilinear variants of maurey and pietsch theorems and applications we prove composition results for multilinear operators and multilinear variants of maurey and pietsch theorems both for multiple p summing p dominated and p summing multilinear operators

optimal output feedback control of discrete linear singularly perturbed stochastic systems the static output feedback control problem for discrete linear singularly perturbed stochastic systems is studied a recursive algorithm is presented to solve the corresponding coupled non linear algebraic equations the algorithm removes the ill conditioning by decomposing the higher order equations into lower order equations and develops a technique which enables us to obtain an arbitrary accuracy that is 0 ej j 1 2 3 a approximation for this problem a numerical example is presented to support the theoretical results communicated by professor a a ioannou

singular perturbation of strictly positive realness abstract the robustness of the strictly positive real spr condition of linear time invariant multi input multi output lti mimo singularly perturbed systems is examined a necessary and sufficient condition under which the full system is spr is proved this robustness result is an extension of the analysis for the popov kalman yakubovich lemma by v r saksena and p v kokotovic 7

reverse inclusions for multiple summing operators abstract multiple summing operators have been proven to be useful in several areas of analysis and mathematical physics in this paper we prove reverse inclusions for this class of operators completing the work already initiated in d perez garcia the inclusion theorem for multiple summing operators studia math 165 3 2004 275 290

fast suboptimal solution to the static output control problem of linear singularly perturbed systems abstract the reduced order suboptimal solution to the static output control problem of linear singularly perturbed system is obtained in terms of the fast variables only assuming the special structure of initial conditions for the slow and fast variables the problem of big initial conditions of the fast variables is considered

unstable rational function approximation the problem is considered of approximating a transfer function with stable and unstable poles by a lower order transfer function with the same number of unstable poles a method is suggested and compared with alternative known methods based on hankel norm approximation examples suggest that no one method always outperforms other methods in terms of minimizing the approximation error

feedback systems and multiple time scales we study feedback design for systems with multiple time scale structure uncovering an intrinsic time scale structure for a state feedback system with full state output from this we construct a multiple time scale asymptotic observer and consider a system with state feedback via a two time scale asymptotic observer finally we obtain more general results for a restricted class of systems

the discrete time h sub spl infin control problem with strictly proper measurement feedback this paper is concerned with the discrete time h sub spl infin control problem with strictly proper measurement feedback we derive necessary and sufficient conditions for the existence of a strictly proper compensator which achieves a given h sub spl infin norm bound note that contrary to the continuous time in discrete time there might exist a suitable proper compensator but no suitable strictly proper compensator finally we give an explicit formula for one controller which achieves this bound

on the design of stabilizing controllers for singularly perturbed systems the robustness of output feedback control designs for singularly perturbed systems based on the reduced systems is discussed a frequency domain approach is presented to determine the conditions for the stability of linear time invariant systems subject to neglected high frequency dynamics in contrast with the qualitative analyses for robust stability that have appeared in the literature this approach gives an explicit computable bound on unmodeled dynamics which does not destabilize the systems stability conditions for various feedback control schemes are presented it is noted that the approach extended to systems with mixed singular regular perturbations can be used to derive the robust stability condition

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods