further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

nonlinear control of constrained linear systems via predictive reference management a method based on conceptual tools of predictive control is described for solving set point tracking problems wherein pointwise in time input and or state inequality constraints are present it consists of adding to a primal compensated system a nonlinear device called command governor cg whose action is based on the current state set point and prescribed constraints the cg selects at any time a virtual sequence among a family of linearly parameterized command sequences by solving a convex constrained quadratic optimization problem and feeds the primal system according to a receding horizon control philosophy the overall system is proved to fulfill the constraints be asymptotically stable and exhibit an offset free tracking behavior provided that an admissibility condition on the initial state is satisfied though the cg can be tailored for the application at hand by appropriately choosing the available design knobs the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem

an analysis and design method for discrete time linear systems under nested saturation this paper considers a discrete time linear system under nested saturation nested saturation arises for example in systems with actuators subject to both magnitude and rate saturation a condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant moreover this condition is shown to be equivalent to linear matrix inequalities lmis in the actual and auxiliary feedback gains as a result the estimation of the domain of attraction for a given set of feedback gains is then formulated as an optimization problem with lmi constraints by viewing the feedback gains as extra free parameters the optimization problem can be used for controller design

a new look at the john nirenberg and john stromberg theorems for bmo abstract we develop some techniques for studying various versions of the function space bmo special cases of one of our results give alternative proofs of the celebrated john nirenberg inequality and of related inequalities due to john and to wik our approach enables us to pose a simply formulated geometric question for which an affirmative answer would lead to a version of the john nirenberg inequality with dimension free constants

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

new relationships between input output and lyapunov stability in this note we define a concept called small signal l p stability and show its relationship to lyapunov stability

semi global stabilization of minimum phase nonlinear systems in special normal forms abstract we semi globally stabilize certain minimum phase nonlinear systems which are in a normal form where the nonlinear subsystem is driven by an output of a linear system that possesses possibly nonzero peaking exponents we eliminate the peaking phenomenon by stabilizing part of the linear system with a high gain linear control and part of the linear system with a small bounded control the interpretation of this approach will be that we are redefining the outputs to add asymptotically stable nonlinear zeros to the system in a manner that allows the new composite zero dynamics to be asymptotically stable on arbitrarily large compact sets

duality and linear programs for stability and performance analysis of queuing networks and scheduling policies we consider the problems of performance analysis and stability instability determination of queuing networks and scheduling policies we exhibit a strong duality relationship between the performance of a system and its stability analysis via mean drift we obtain a variety of linear programs lps to conduct such stability and performance analyses a certain lp called the performance lp bounds the performance of all stationary nonidling scheduling policies if it is bounded then its dual called the drift lp has a feasible solution which is a copositive matrix the quadratic form associated with this copositive matrix has a negative drift showing that all stationary nonidling scheduling policies result in a geometrically converging exponential moment these results carry over to fluid models allowing the study of networks with nonexponential distributions if a modification of the performance lp called the monotone lp is bounded then the system is stable finally there is a another modification of the performance lp called the finite time lp it provides transient bounds on the performance of the system from any initial condition

a gauss seidel type solver for the fast computation of input constrained control systems abstract an important class of nonlinear control systems can be represented as the feedback interconnection of two parts a linear time invariant system and a block of decentralized nonlinearities when the linear time invariant part has a nontrivial feedthrough term or the nonlinearity has a feedback gain control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant the requirements for such online computation may result in several implementation issues especially in real time and embedded control applications this paper considers the implementation of such algebraic loops arising from several input constrained systems the proposed solution algorithm is globally convergent for a very large class of feedthrough or feedback gains and shows promise for real time and embedded control applications where a fast but approximate solution is of the essence

inherent observer property in a class of anti windup compensators owing to the types of non linearities involved the analysis and the comparison of different anti windup compensators that are available in the literature become difficult towards achieving a better understanding of the mechanisms of these anti windup compensators we here expose the observer property inherent in a class of anti windup compensators this observer property allows us to unify these anti windup compensators as special cases of the generalized anti windup compensator due to astrom and wittenmark 1984 and provides a general framework to investigate their performance

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

semi global stabilization of discrete time linear systems with position and rate limited actuators it is shown via explicit construction of feedback laws that if a discrete time linear system is asymptotically null controllable with bounded controls then when subject to both actuator position and rate saturation it is semi globally stabilizable by linear state feedback if in addition the system is also detectable then it is semi globally stabilizable via linear output feedback

siso linear system control via saturating actuator l2 tracking performance in the presence of arbitrary shaped inputs most studies on linear system control in the presence of actuator saturation have focused on closed loop asymptotic stabilisation available tracking results are generally limited to constraint compatible inputs references disturbances with known exogenous input models the problem of output reference tracking in the presence of arbitrary shaped not necessarily constraint compatible inputs has yet to be investigated in this study we show that an tracking performance is achievable for siso linear systems using a given class of saturated controllers accordingly the tracking error energy resp power is bounded by the energy resp power of a well defined mismatch input depending on the disturbance and reference compatibility in the disturbance free case this entails perfect asymptotic tracking of arbitrary shaped constraint compatible reference signals otherwise the average tracking quality is proportional to the mismatch input power in the case of periodic inputs constraint compatible or not

simple saturated designs for ancbc systems and extension to feedforward nonlinear systems this article re examines the robust stabilisation of the asymptotically null controllable with bounded controls ancbc systems and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators based on the notion of converging input bounded state cibs rather than small input small state siss the computation burden in sussmann et al sussmann h j sontag e d and yang y 1994 a general result on the stabilization of linear systems using bounded controls ieee transactions on automatic control 39 2411 2425 is reduced and a class of simple saturated control laws is presented for the cibs stabilisation of ancbc systems then by combining the technique of dealing with higher order terms the algorithm for ancbc systems is extended to feedforward nonlinear systems

a magnitude and rate saturation model and its use in the solution of a static anti windup problem in this paper we address the anti windup design problem for linear control systems with strictly proper controllers in the presence of input magnitude and rate saturation using generalized sector condition we provide an lmi based procedure for the construction of a linear anti windup gain acting on the controller state equation such that regional closed loop stability is guaranteed and suitable performance measures are optimized the approach is successfully illustrated on a simulation example

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

the structure of bandlimited bmo functions and applications abstract in this paper we analyze the structure of bandlimited bmo functions using a recently found equation for the calculation of the hilbert transform of bounded bandlimited functions we derive a decomposition result for bandlimited bmo functions which is similar to the well known fefferman stein decomposition based on this decomposition we characterize the range of the hilbert transform moreover we present interesting applications of this result we characterize the peak value behavior of bandlimited bmo functions show that the derivative of bandlimited bmo functions is bounded and prove a sampling theorem for bandlimited bmo functions

anti windup synthesis for systems with rate limits using riccati equations this article develops an anti windup aw scheme for systems with rate limited actuators the main results show how a full order aw compensator can be synthesised using an algebraic riccati equation and several free parameters a further result then shows how the free parameters may be chosen to influence in an intuitive way the local gain of the system and the size of the region of attraction the results are of interest due to their low computational burden and hence their applicability to the systems of large state dimension

l2 anti windup for linear dead time systems in this paper we address and solve the problem of antiwindup augmentation for linear systems with input and output delay in particular we give a formal definition of the anti windup construction problem in the global local robust and nominal cases for each of these cases we show that a specific anti windup compensation structure which is a generalization of the approach in 131 is capable of solving the anti windup problem whenever this is solvable the effectiveness of the proposed scheme is shown on a simple example taken from the literature in which the plant is a marginally stable linear system the anti windup design problem has been qualitatively stated already from the 1950 s both in the analog and in the digital control framework however the arisin solutions were at that time mainly application oriente and not applicable to large classes of control systems it was only in the 1980 s that some design techniques ap plicable to large classes of control systems were formalized although the issue of performance characterization and improvement was still mostly unsolved an interestin survey of these techniques can be found in 141 anotier dhenomenon that is often found in coninnction

design of saturation based switching anti windup gains for the enlargement of the domain of attraction this technical note proposes a saturation based switching anti windup design for the enlargement of the domain of attraction of the closed loop system a widely adopted method of dealing with an m dimensional saturated linear feedback is to express it as a linear combination of a set of 2m auxiliary linear feedbacks for each value of the state these auxiliary linear feedbacks form a convex polyhedron of 2m vertices in the input space we propose to divide this convex polyhedron into several convex sub polyhedrons each of which is defined as the convex hull of a subset of the auxiliary feedbacks whenever the value of the saturated linear feedback falls into a sub polyhedron it can be expressed as a linear combination of a subset of the 2m auxiliary linear feedbacks that define the sub polyhedron and thus a less conservative result can be expected a separate anti windup gain is designed for each sub polyhedron by using a common quadratic lyapunov function and implemented when the value of the saturated linear feedback falls into this sub polyhedron simulation results indicate that such a saturation based switching anti windup design has the ability to significantly enlarge the domain of attraction of the closed loop system

adaptive boundary control of a flexible manipulator with input saturation abstractin this study we consider the anti windup design as one of the approaches for the boundary control problem of a flexible manipulator in the presence of system parametric uncertainties external disturbances and bounded inputs the dynamics of the system are represented by partial differential equations pdes using the singular perturbation approach the pde model is divided into two simpler subsystems with the lyapunov s direct method an adaptive boundary control scheme is developed to regulate the angular position and suppress the elastic vibration simultaneously and the adaptive laws are designed to compensate for the system parametric uncertainties and the disturbances the proposed control scheme allows the application of smooth hyperbolic functions which satisfy physical conditions and input restrictions be easily realised numerical simulations demonstrate the effectiveness of the proposed scheme

nonlinear scheduled anti windup design for linear systems the nonlinear l sub 2 anti windup framework introduced in teel and kapor 1997 reduces the anti windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched l sub 2 disturbances in this note based on the structure proposed in that previous paper we provide a linear matrix ineqaulity lmi formulation of high performance anti windup design for control systems with linear asymptotically stable plants in particular we first give a linear quadratic based formulation of linear anti windup compensation in terms of the solution of a set of always feasible lmi constraints then we propose a nonlinear scheduling technique where hysteresis switching among a family of linear gains is employed for performance improvement both design techniques are demonstrated on an academic example

an analysis and design method for linear systems under nested saturation this paper considers a linear system under nested saturation nested saturation arises for example when the actuator is subject to magnitude and rate saturation simultaneously a condition is derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant moreover this condition is shown to be equivalent to linear matrix inequalities lmis in the actual and auxiliary feedback gains as a result the estimation of the domain of attraction for a given set of feedback gains can be formulated as an optimization problem with lmi constraints by viewing the feedback gains as extra free parameters the optimization problem can be used for controller design

generalized sector synthesis of output feedback control with anti windup structure this paper considers the control synthesis problem for linear time invariant lti continuous time systems with actuator saturation nonlinearities the control architecture is standard a nominal lti output feedback with an anti windup aw mechanism traditional approaches have focused on aw synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the aw compensator is added to guarantee stability performance properties when the actuators saturate in contrast this paper proposes a synthesis method to design both the nominal controller and the aw compensator simultaneously using the generalized sector gs approach in the multiplier setting a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed loop system our result is shown to include the existing results on the simultaneous circle synthesis and the anti windup gs synthesis as special cases this paper also shows that the direct feed through term in the aw compensator does not contribute to enlarging the achievable domain of attraction within the multiplier gs framework

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

equivalence between classes of multipliers for slope restricted nonlinearities different classes of multipliers have been proposed in the literature for obtaining stability criteria using passivity theory integral quadratic constraint iqc theory or lyapunov theory some of these classes of multipliers can be applied with slope restricted nonlinearities in this paper the concept of phase containment is defined and it is shown that several classes are phase contained within the class of zames falb multipliers there are two main consequences firstly it follows that the class of zames falb multipliers remains to date the widest class of available multipliers for slope restricted nonlinearities secondly further restrictions may be avoided when exploiting the parametrization of the other classes of multipliers

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

semi global stabilization of partially linear composite systems via feedback of the state of the linear part abstract we consider the problem of semi global stabilization of a class of partially linear composite systems we show by explicit construction of the control laws that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi globally stabilizable by a dynamic feedback of the state of the linear subsystem if a the linear subsystem is right invertible and has all its invariant zeros in the closed left half s plane and b the only linear variables entering the nonlinear subsystem are the output of the linear subsystem our work generalizes previous results by c i byrnes and a isidori 1991 h j sussmann and p v kokotovic 1991 and a r teel 1992

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

a non square sector condition and its application in deferred action anti windup compensator design a sector condition for two connected deadzone nonlinearities is provided by introducing an additional non square operator which exploits their connectivity a more general set of sector like matrix inequalities is obtained this non square matrix inequality condition is applied to an anti windup aw problem in which the aw compensator is not activated until the unconstrained control signal reaches a well defined level beyond that of the physical actuator limits the non square sector condition allows such deferred action aw synthesis to be performed in a manner much closer to traditional immediate sector based aw with either lowered conservatism or decreased computational effort in contrast to recent work the non square condition is applicable to other aw problems

global analysis of piecewise linear systems using impact maps and surface lyapunov functions this paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems pls this methodology infers global properties of pls solely by studying the behavior at switching surfaces associated with pls the main idea is to analyze impact maps i e maps from one switching surface to the next switching surface such maps are known to be unfriendly maps in the sense that they are highly nonlinear multivalued and not continuous we found however that an impact map induced by an linear time invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state this representation of impact maps allows the search for surface lyapunov functions sulf to be done by simply solving a semidefinite program allowing global asymptotic stability robustness and performance of limit cycles and equilibrium points of pls to be efficiently checked this new analysis methodology has been applied to relay feedback on off and saturation systems where it has shown to be very successful in globally analyzing a large number of examples in fact it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology examples analyzed include systems of relative degree larger than one and of high dimension for which no other analysis methodology could be applied this success in globally analyzing certain classes of pls has shown the power of this new methodology and suggests its potential toward the analysis of larger and more complex pls

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

global stabilization of classes of linear control systems with bounds on the feedback and its successive derivatives in this paper we address the problem of globally stabilizing a linear time invariant lti system by means of a static feedback law whose amplitude and successive time derivatives up to a prescribed order p are bounded by arbitrary prescribed values we solve this problem for two classes of lti systems namely integrator chains and controllable skew symmetric systems with single input for the integrator chains the solution we propose is based on the nested saturations introduced by a r teel we show that this construction fails for skew symmetric systems and propose an alternative feedback law we illustrate these findings by the stabilization of the third order integrator and the harmonic oscillator with prescribed bounds on the feedback and its first two derivatives

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

dynamic output feedback compensation for linear systems with independent amplitude and rate saturations the positive real lemma provides the basis for constructing linear output feedback dynamic compensators for multi input plants with independent amplitude saturations fixed structure techniques are used to obtain full and reduced order feedback compensators along with a guaranteed domain of attraction these results are then applied to the problem of rate saturation by using a feedback type model rate saturation is modelled as an amplitude saturation the closed loop system with amplitude and rate saturation is then treated as a system with independent amplitude saturations

sharp multiplicative inequalities with bmo i abstract we find the best possible constant c in the inequality l r c l p p r bmo 1 p r where 2 r and p r we employ the bellman function technique to solve this problem in the case of an interval and then transfer our results to the circle and the line

sharp results in the integral form john nirenberg inequality we consider the strong form of the john nirenberg inequality for the l 2 based bmo we construct explicit bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant as well as the precise bound on the inequality s range of validity both previously unknown the results for the two cases are substantially different the paper not only gives another instance in the short list of such explicit calculations but also presents the bellman function method as a sequence of clear steps adaptable to a wide variety of applications

system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

the mean number in system vector range for multiclass queueing networks in a multiclass network of queues natural sufficient conditions are given for the mean number in system vector to cover the nonnegative orthant as the arrival rate vector varies over the stable domain

a new perspective on static and low order anti windup synthesis by viewing the anti windup problem as a decoupled set of subsystems and relating this configuration to a general static anti windup set up lmi conditions are established which guarantee stability and performance of the resulting closed loop system the approach taken and the mapping used for the performance index are logical and intuitive and it is argued central to the true anti windup objective the approach enables one to construct static anti windup compensators in a systematic and numerically tractable manner the idea is extended to allow low order anti windup compensators to be synthesized which while being sub optimal can improve transient performance and possess several desired properties such as low computational overhead and sensible closed loop pole locations in addition low order anti windup synthesis is often feasible when the corresponding static synthesis is not

assignable polynomials to linear systems over von neumann regular rings abstract given a system a b over a commutative von neumann regular ring r it is proved that there exist a matrix f and a vector u such that the single input system a b f b u and the original system a b have the same module of reachable states and the same set of polynomials assignable by state feedback moreover there is a bijection between reachable states and assignable polynomials in the form of a certain isomorphism of r modules and the existence of this isomorphism for all systems actually characterizes von neumann regular rings finally the set of assignable polynomials to a single input system is completely described for arbitrary commutative rings which in the case of von neumann regular rings completes the study of assignable polynomials to multi input systems

linear lmi based external anti windup augmentation for stable linear systems we study linear anti windup augmentation for linear control systems with saturated linear plants in the special case when the anti windup compensator can only modify the input and the output of the windup prone linear controller we also measure the arising performance in terms of the finite l 2 gain from exogenous inputs to selected performance outputs our main results are a system theoretic feasibility characterization for fixed order anti windup design and a linear matrix inequality lmi formulation for optimal static and plant order anti windup design interpretations of lower bounds on the achievable performance are also given the effectiveness of the design procedure is demonstrated on a simulation example

a partial parameterization of nonlinear output feedback controllers for saturated linear systems this paper addresses the stabilization problem of linear systems subject to input saturation the major purpose is to introduce nonlinearity into control laws so as to expand the design freedom for performance enhancement to this end a new approach is developed which involves a partial differential matrix inequality pdmi a class of stabilizing feedback laws is explicitly obtained by solving this pdmi analytically and the feedback laws are parameterized by a nonlinear function further it is revealed that any linear observer can be used to realize the output feedback stabilization numerical examples including the seek control of a hard disk drive show that the introduced nonlinearity does contribute to the improvement of system performance the application to integral control is also discussed

uniting local and global output feedback controllers we consider control systems for which we know two stabilizing output feedback controllers one is globally asymptotically stabilizing while the other one is only locally asymptotically stabilizing we look for a composite output feedback control law that is equal to the local feedback on a neighborhood of the origin and that is globally asymptotically stabilizing since we want some robustness with respect to measurement noise actuator errors and external disturbances we need to consider hybrid output feedback controllers under an input output to state stability assumption we exhibit a solution of this uniting problem by means of a dynamic hybrid output feedback controller then we particularize our study to linear control systems with saturation at the input for which we know two stabilizing output feedback controllers one is a nonlinear globally asymptotically stabilizing controller while the other one is a high performance linear only locally asymptotically stabilizing controller we specify numerically tractable conditions to solve this uniting problem finally we illustrate our main results by means of numerical examples

brief paper anti windup synthesis for linear control systems with input saturation achieving regional nonlinear performance in this paper we present lmi based synthesis tools for regional stability and performance of linear anti windup compensators for linear control systems we consider both static and dynamic compensators algorithms are developed that minimize the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and that minimize this upper bound with a guaranteed reachable set or domain of attraction based on the structure of the optimization problems it is shown that for systems whose plants have poles in the closed left half plane plant order dynamic anti windup can achieve semiglobal exponential stability and finite l 2 gain for exogenous inputs with l 2 norm bounded by any finite value the problems are studied in a general setting where the only requirement on the linear control system is well posedness and internal stability the effectiveness of the proposed techniques is illustrated with an example

robust anti windup controller design of time delay fuzzy systems with actuator saturations this study presents a robust anti windup fuzzy control approach for uncertain nonlinear time delay systems with actuator saturations the discussed system dynamics is presented by the takagi sugeno t s fuzzy model to facilitate the design process the nonlinearity of input saturation is characterized by a specific sector condition given a stabilizing dynamic output feedback fuzzy controller an anti windup control approach is then developed to maximize the size of estimate of the domain of attraction significantly the convergence of all admissible initial states within this region could be ensured based on the lyapunov krasovskii delay independent and delay dependent analyses sufficient conditions for the robust stabilization are derived these conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities allowing the fuzzy controller to be synthesized more efficiently finally numeric simulations are given to validate the proposed approach

brief multiplier theory for stability analysis of anti windup control systems we apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti windup bumpless transfer awbt schemes for appropriate choices of the multipliers we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities lmis we show that a number of previously reported attempts to analyze awbt stability using seemingly diverse techniques such as the popov circle and off axis circle criteria the optimally scaled small gain theorem generalized m upper bound and describing functions can all be generalized within the framework of this paper

analysis and design for discrete time linear systems subject to actuator saturation we present a method to estimate the domain of attraction for a discrete time linear system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis the following surprising result is revealed for systems with single input suppose that an ellipsoid is made invariant with a linear feedback then it is invariant under the saturated linear feedback if and only if there exists a saturated nonlinear feedback which makes the ellipsoid invariant finally the set invariance condition is extended to determine invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements

linear discrete time global and regional anti windup an lmi approach in this article we address linear anti windup design for linear discrete time control systems guaranteeing regional and global stability and performance the techniques that we develop are the discrete time counterpart of existing techniques for anti windup augmentation which lead to convex constructions by way of linear matrix inequalities lmis when adopting static and plant order anti windup augmentation interesting system theoretic interpretations of the performance bounds for the non linear closed loop can also be given we show here that parallel results apply to the discrete time case we derive the corresponding conditions and prove their effectiveness by adapting the continuous time approaches to the discrete time case

convex design of a robust antiwindup controller for an lft model in the context of a closed loop lft model an lmi technique is proposed for the synthesis of a static or dynamic antiwindup controller which can be seen as a nontrivial extension of existing lmi methods for designing a robust filter or feedforward controller a missile example is given to illustrate the feasibility of the technique

a class of onto multifunctions a convex valued upper continuous multifunction with pointed closed convex domain is proved to be onto if there is a selection with certain coercive properties and if the selection for each point lies in the affine hull of the smallest face of the domain containing the point the proof uses a piecewise affine homotopy construction we apply the onto theorem to an approximation of a network of servers and show that arbitrary congestion levels can be realized with appropriate arrival levels

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

a framework for multivariable algebraic loops in linear anti windup implementations abstract this brief paper addresses the implementation and well posedness aspects of multivariable algebraic loops which arise naturally in many anti windup control schemes using the machinery of linear complementarity problems a unified framework is developed for establishing well posedness of such algebraic loops enforcing well posedness is reduced to a linear matrix inequality feasibility problem that can be solved during the anti windup design stage several existing anti windup implementations appear as special cases of the unified framework presented in this brief paper

anti windup synthesis using riccati equations the aim of this paper is to give a novel solution to the full order anti windup aw compensation problem for stable systems with input saturation the solution is obtained by completing the square in three steps and requires the solution to a single bounded real riccati equation characterized by the open loop plant s norm the riccati equation plays the role of the lmis usually found in anti windup synthesis but in addition to its numerical advantages it yields a family of anti windup compensators with the same performance this family of compensators is parameterized by a matrix which is intimately linked with both the poles of the anti windup compensator and the robustness properties of the closed loop saturated system thus this matrix allows a robust anti windup problem to be solved in a straightforward and intuitive manner the effectiveness of the proposed technique is demonstrated on a simple example

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

piecewise quadratic lyapunov functions for systems with deadzones or saturations a piecewise quadratic lyapunov function is developed for the analysis of the global and regional performances for systems with saturation deadzone in a general feedback configuration with an algebraic loop this piecewise quadratic lyapunov function effectively incorporates the structure of the saturation deadzone nonlinearity several sector like conditions are derived to describe the complex nonlinear algebraic loop these conditions transform several performance analysis problems into optimization problems with linear or bilinear matrix inequalities the effectiveness of the results is demonstrated with numerical examples

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

limitations on the stabilizability of globally minimum phase systems the author gives examples showing that in general it is possible for a globally minimum phase system in normal form to have states that cannot be driven asymptotically to the origin by means of any open loop control in particular this provides counterexamples to a number of recently published stabilization theorems it is established by means of examples that a minimum phase system in normal form need not be semiglobally stabilizable or small input semiglobally bibo stabilizable even if the zero dynamics is exponentially stable and the completeness condition holds

dynamic output feedback for discrete time systems under amplitude and rate actuator constraints this work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete time linear systems with rate and amplitude saturating actuators the nonlinear effects introduced by the saturations in the closed loop system are taken into account by using a generalized sector condition which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities

a rearranged good inequality let tf be a maximal calderon zygmund singular integral mf the hardy littlewood maximal function and w an aoo weight we replace the good a inequality w x tf x 2r and mf x a by the rearrangement inequality tf t c mt t 2 tf 2t and show that it gives better estimates for tf in particular we obtain best possible weighted lp bounds previously unknown exponential integrability estimates and simplified derivations of known unweighted estimates for tf

brief paper output feedback design for saturated linear plants using deadzone loops in this paper we present an lmi based synthesis approach on output feedback design for input saturated linear systems by using deadzone loops algorithms are developed for minimizing the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and for minimizing this upper bound with a guaranteed reachable set or domain of attraction the proposed synthesis approach will always lead to regionally stabilizing controllers if the plant is exponentially unstable to semi global results if the plant is non exponentially unstable and to global results if the plant is already exponentially stable where the only requirement on the linear plant is detectability and stabilizability the effectiveness of the proposed techniques is illustrated with one example

brief paper an anti windup technique for lmi regions the anti windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time invariant plant and controller this paper presents a linear matrix inequality lmi based method that attempts to minimize performance deterioration while explicitly restricting the anti windup closed loop dynamics the restriction placed on the dynamics is described via lmi regions which is a form of regional pole placement finally the techniques discussed in this paper are demonstrated on an electro hydraulic testbed

observer based anti windup compensator design for saturated control systems using an lmi approach in practical control systems actuator saturation usually induces a windup phenomenon and potentially results in system instability accordingly this paper develops an observer based auxiliary anti windup compensation scheme to mitigate the effects of actuator limitations on the performance and stability of the controlled system in the proposed approach the controller output signal passing through the saturation element is treated as an external disturbance imported to the designed controller and an auxiliary controller is designed to minimize the difference between the controller output signal and the system input signal the conditions required to maintain the system performance in the presence of actuator saturation are formulated as an lmi criterion the l 2 stability criterion of the anti windup compensator design is also formulated as an lmi condition it is shown that by integrating the two lmi conditions and solving the resulting optimization problem the resulting anti windup controller both minimizes the performance attenuation of the saturated control system and guarantees its l 2 stability

integrator backstepping for rounded controls and control rates we present a backstepping procedure for the design of globally stabilizing state feedback control laws such that the magnitudes of the control signals and their derivatives are bounded by constants which do not depend on the initial conditions we accomplish this by propagating such boundedness properties through each step of the recursive design

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

synthesis of stabilizing antiwindup controllers using piecewise quadratic lyapunov functions we consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in kothare automatica vol 30 no 12 pp 1869 1883 1994 applicable to linear time invariant systems lti subject to a saturating actuator our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus we can utilize piecewise quadratic lyapunov function theory johansson and rantzer ieee trans autom control vol 43 no 4 pp 555 559 apr 1998 rantzer and johansson ieee trans autom control vol 45 no 4 pp 629 637 apr 2000 and johansson proc 14th world congr beijing china 1999 pp 521 5260 to determine a stabilizing antiwindup control law the synthesis problem is expressed in terms of bilinear matrix inequalities bmis and is solved using an iterative approach as well as using commercial software the performance of the system is optimized by minimizing an upper bound on the induced gain of the system the proposed approach is demonstrated using examples

robust stabilizing controller design for takagi sugeno fuzzy descriptor systems under state constraints and actuator saturation abstract the aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by takagi sugeno fuzzy descriptor systems and subject to input and state constraints for this a novel structure of modified parallel distributed compensation control laws is proposed the controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from lyapunov s stability theory and the choice of an original lyapunov function this ensures the stabilization of the closed loop system and the respect of the state and input constraints regionally the technique is illustrated through three numerical examples

the l2 anti windup problem for discrete time linear systems definition and solutions abstract the anti windup problem for discrete time linear systems is formalized in terms of the l 2 norm of the deviation of the actual response of the system with saturation and anti windup compensation from the ideal unconstrained response we show that paralleling continuous time results a r teel n kapoor the l 2 anti windup problem its definition and solution in proceedings of the 4th ecc brussels belgium july 1997 the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable we provide a constructive solution whenever the problem is solvable also offered is a high performance global solution for exponentially stable plants based on receding horizon control illustrative simulations are included

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

a novel approach to control of nonminimum phase nonlinear systems we present an approach to control of nonminimum phase multiple input multiple output mimo nonlinear systems based on a singular perturbation like technique first we show that a mimo nonlinear system can be converted into a singularly perturbed system through magnitude and time scaling transformation in particular the proposed transformation technique can make the hidden or internal dynamics behave like a fast subsystem however the fast subsystem takes a weakly controllable form which implies that a small positive low gain parameter multiplies the control input in the fast subsystem for this reason the well known integral manifold approach is then utilized to decompose the resulting singularly perturbed system into two subsystems in separate timescales each of which is of a lower dimension and more importantly controllable in the sense that the control input will explicitly appear in the boundary layer system the proposed method is particularly useful to make the input output dynamic characteristics of a decouplable nonminimum phase nonlinear system decoupled and linear

anti windup based dynamic controller synthesis for nonlinear systems under input saturation this paper describes the design of dynamic controller and static anti windup compensator awc for lipschitz nonlinear systems under input saturation global and local awc based control schemes for stabilization of the nonlinear systems are proposed and necessary conditions for feasibility of the control approaches are investigated a one step approach for simultaneous design of h controller and awc by means of linear matrix inequalities lmis is presented herein which supports multi objective synthesis to attain stabilization or tracking robustness against disturbance and noise and penalization of large and high frequency control signals this multi objective synthesis can be accomplished by incorporating design weights as commonly used in the standard h control theory to design a performance oriented anti windup based control scheme lmis for the global control of the nonlinear systems subject to input saturation are derived by application of a quadratic lyapunov function the lipschitz condition the global sector condition l 2 gain reduction substantial matrix algebra and variable transformation in order to cope with unstable and oscillatory nonlinear systems lmi based local results are established using a local sector condition additional conditions are derived by incorporating properties of the saturation function to ensure well posedness of the controller two simulation examples are provided to show the effectiveness of the proposed control schemes for control of stable and chaotic nonlinear systems under input saturation

anti windup control design for exponentially unstable lti systems with actuator saturation in this paper a new saturation control technique in the framework of anti windup compensation is developed for exponentially unstable linear time invariant systems subject to input nonlinearities the proposed control algorithm guarantees regional stability in the existence of input saturation and provides less conservative performance than most existing anti windup schemes moreover an explicit form of anti windup controller with its order no more than the order of the plant is derived an inverted pendulum example is used to demonstrate the advantages of the newly proposed anti windup control technique

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

brief paper simultaneous linear and anti windup controller synthesis using multiobjective convex optimization we present a method for the synthesis of a control law for input constrained linear systems that incorporates both a traditional linear output feedback controller as well as a static anti windup compensator unlike traditional two step anti windup controller designs in which the linear controller and anti windup compensator are designed sequentially our method synthesizes all controller parameters simultaneously this one step design retains the anti windup structure thus providing structurally a priori compensation for saturation we derive sufficient conditions for guaranteeing global quadratic stability and for satisfying multiple possibly conflicting performance objectives on the constrained and unconstrained closed loop dynamics the resulting synthesis problem is recast as an optimization over linear matrix inequalities lmis we demonstrate the proposed method on a benchmark problem

local stabilization of discrete time linear systems with saturating controls an lmi based approach deals with the problem of local stabilization of linear discrete time systems subject to control saturation a linear matrix inequalities based framework is proposed in order to compute a saturating state feedback that stabilizes the system with respect to a given set of admissible initial states and in addition guarantees some dynamical performances when the system operates in the zone of linear behavior i e when the controls are not saturated

anti windup synthesis via sampled data piecewise affine optimal control discrete time receding horizon optimal control is employed in model based anti windup augmentation the optimal control formulation enables designs that minimize the mismatch between the unconstrained closed loop response with a given controller and the constrained closed loop response with anti windup augmentation recently developed techniques for off line computation of the constrained linear regulator s solution which is piecewise affine facilitate implementation the resulting sampled data anti windup closed loop system s properties are established and its performance is demonstrated on a simulation example

formulation of linear problems and solution by a universal machine using the predicate language for ordered fields a class of problems referred to aslinear problems is defined this class contains for example all systems of linear equations and inequalities all linear programming problems all integer programming problems with bounded variables all linear complementarity problems the testing of whether sets that are defined by linear inequalities are semilattices all satisfiability problems in sentenial logic the rank computation of matrices the computation of row reduced echelon forms of matrices and all quadratic programming problems with bounded variables a single one algorithm to which we refer as theuniversal linear machine is described it solves any instance of any linear problem the universal linear machine runs in two phases given a linear problem in the first phase a compiler running on a turing machine generates alinear algorithm for the problem then given an instance of the linear problem in the second phase the linear algorithm solves the particular instance of the linear problem the linear algorithm is finite deterministic loopless and executes only the five ordered field operations additions multiplications subtractions divisions and comparisons conversely we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely finally it is shown that with a linear algorithm for a linear problem one can solve certain parametric instances of the linear problem