l_ infty and l_ 2 low gain feedback their properties characterizations and applications in constrained control low gain feedback has found several applications in constrained control robust control and nonlinear control in this paper we first generalize the existing low gain design methods by introducing the notion of l vanishment and by providing a full characterization of feedback gains that achieve such a property we observe that l low gain feedback can lead to energy peaking namely the control energy required by l low gain feedback increases toward infinity as the low gain parameter decreases to zero motivated by this observation we consider the notion of l2 vanishment and establish several of its characterizations based on which a new design approach referred to as the l2 low gain feedback approach for linear systems is developed different from the l low gain feedback the l2 low gain feedback is instrumental in the control of systems with control energy constraints as an application of l2 low gain feedback the problem of semiglobal stabilization of linear systems with control energy constraints is solved in this paper the notions of l and l2 vanishment also allow us to establish a systematic approach to the design of l and l2 low gain feedback the advantage of this new design approach is that it results in a family of control laws including those resulting from the existing design methods

designing stabilizing controllers for uncertain systems using the riccati equation approach a useful technique for determining a linear feedback control law stabilizes an uncertain system is the riccati equation approach of i r petersen and c v hollot 1986 they consider systems with time varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a riccati equation the technique is extended to include problems with time varying uncertainty in the input connection matrix several examples are included to demonstrate the efficacy of this result

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

digital filter design using root moments for sum of all pass structures from complete and partial specifications this paper is concerned with the development of digital filter design procedures for transfer functions in the form of sum of all pass in which the requirements may be partially specified specifically the requirements for a digital filter or equalizer in amplitude a spl theta or phase spl phi spl theta or possibly group delay response spl tau spl theta may be specified from measurements over a limited a set of frequencies spl theta sub 1 spl theta sub 2 the problem is to develop techniques for the design a transfer function h z satisfying these specifications and constrained to be in the form of a sum of two all pass functions the proposed solution is based on the use of root moments the companion problem concerned with the estimation of the orders of the required all pass filters is also examined and a solution proposed based on the same context of root moments

brief paper a new concept of invariance for saturated systems in this paper the notions of sns invariance and sns domain of attraction are introduced the sns domain of attraction serves as an estimation of the domain of attraction of a saturated system it is shown that in the case of single input saturated systems any contractive set is contained in the sns domain of attraction another important characteristic of the sns domain of attraction is that it contains any estimation obtained by means of a linear difference inclusion of the saturated system a simple algorithm that converges to the sns domain of attraction is presented an illustrative example is given

anti disturbance control for nonlinear systems subject to input saturation via disturbance observer this paper is concerned with the problem of the disturbance observer based control for a class of continuous time uncertain systems subject to input saturation and nonlinearity the input of the system includes two parts the control input and the disturbance input the nonlinearity of the system which satisfies a global lipschitz condition is considered as two cases of known nonlinearity and unknown nonlinearity by virtue of the technique of the disturbance observer based controller the anti disturbance controllers are designed respectively with both the polytopic and dead zone representations of the saturation function which ensure that the resulting closed loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the lyapunov function further an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states an example of application design for a flight control system illustrates the effectiveness of the proposed results

an nth step set invariance approach to the analysis and design of discrete time linear systems subject to actuator saturation abstract for a discrete time linear system subject to actuator saturation an analysis and design approach based on n th step set invariance is proposed an n th step invariant set is a set from which all trajectories will enter a contractively invariant set in n steps and thus can be used as an estimate of the domain of attraction such an estimate is less conservative than an estimate obtained on the basis of contractive invariance of ellipsoids which excludes initial conditions from which the trajectories overshoot outside the ellipsoid before converging to the origin in comparison with the existing approach based on conventional set invariance the proposed approach results in a larger domain of attraction and better performance both in the analysis of the closed loop system under a given feedback gain and in the design of feedback gain in comparison with the saturated and nonsaturated sns invariant set approach which is an analysis approach the proposed approach can be used for control design even in the presence of plant uncertainties

analysis and design of discrete time linear systems with nested actuator saturations abstract this paper is concerned with the analysis and design of discrete time linear systems subject to nested saturation functions by utilizing a new compact convex hull representation of the saturation nonlinearity a linear matrix inequalities lmis based condition is obtained for testing the local and global stability of the considered nonlinear system the estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed loop system is maximized are then converted into some lmis based optimization problems compared with the existing results on the same problems the proposed solutions are less conservative as more slack variables are introduced into the conditions a couple of numerical examples are worked out to validate the effectiveness of the proposed approach

local stabilization of linear systems under amplitude and rate saturating actuators this note addresses the problem of local stabilization of linear systems subject to control amplitude and rate saturation considering the actuator represented by a first order system subject to input and state saturation a condition for the stabilization of an a priori given set of admissible initial states is formulated from certain saturation nonlinearities representation and quadratic stability results from this condition an algorithm based on the iterative solution of linear matrix inequalities based problems is proposed in order to compute the control law

semiglobal stabilization of linear discrete time systems subject to input saturation via linear feedback an are based approach we revisit the problem of semiglobal stabilization of linear discrete time systems subject to input saturation and give an algebraic riccati equation are based approach to the proof of a fact established earlier lin and saberi 1995 i e a linear discrete time system subject to input saturation is semiglobally stabilizable via linear feedback as long as the linear system in the absence of the saturation is stabilizable and detectable and all its open loop poles are located inside or on the unit circle moreover we drastically relax the requirements on the characteristic of the saturation elements as imposed in the earlier work

quadratic stability for hybrid systems with nested saturations the problems of characterizing quadratic stability and computing an estimation of the domain of attraction for saturated hybrid systems are addressed hybrid systems presenting saturations and nested saturations on signals involved in both the continuous time and the discrete time dynamics are considered geometrical characterizations of local and global quadratic stability are provided computation oriented conditions for quadratic stability are given in form of convex constraints

on maximizing the convergence rate for linear systems with input saturation in this note we consider a few important issues related to the maximization of the convergence rate inside a given ellipsoid for linear systems with input saturation for continuous time systems the control that maximizes the convergence rate is simply a bang bang control through studying the system under the maximal convergence control we reveal several fundamental results on set invariance an important consequence of maximizing the convergence rate is that the maximal invariant ellipsoid is produced we provide a simple method for finding the maximal invariant ellipsoid and we also study the dependence of the maximal convergence rate on the lyapunov function

anti windup design with guaranteed regions of stability for discrete time linear systems abstract the purpose of this paper is to study the determination of stability regions for discrete time linear systems with saturating controls through anti windup schemes considering that a linear dynamic output feedback has been designed to stabilize the linear discrete time system without saturation a method is proposed for designing an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system in the presence of saturation it is shown that the closed loop system obtained from the controller plus the anti windup gain can be locally modeled by a linear system with a deadzone nonlinearity then based on the use of a new sector condition and quadratic lyapunov functions stability conditions in an lmi form are stated these conditions are then considered in a convex optimization problem in order to compute an anti windup gain that maximizes an estimate of the basin of attraction of the closed loop system moreover considering asymptotically stable open loop systems it is shown that the conditions can be slightly modified in order to determine an anti windup gain that ensures global stability an extension of the proposed results to the case of dynamic anti windup synthesis is also presented in the paper

symplectic and multisymplectic numerical methods for maxwell s equations in this paper we compare the behaviour of one symplectic and three multisymplectic methods for maxwell s equations in a simple medium this is a system of pdes with symplectic and multisymplectic structures we give a theoretical discussion of how some numerical methods preserve the discrete versions of the local and global conservation laws and verify this behaviour in numerical experiments we also show that these numerical methods preserve the divergence furthermore we extend the discussion on dispersion for multi symplectic methods applied to pdes with one spatial dimension to include anisotropy when applying multi symplectic methods to maxwell s equations in two spatial dimensions lastly we demonstrate how varying the courant friedrichs lewy cfl number can cause the multi symplectic methods in our comparison to behave differently which can be explained by the study of backward error analysis for pdes

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

adaptation coordination and local interactions via distributed approachability abstract this paper investigates the relation between cooperation competition and local interactions in large distributed multi agent systems the main contribution is the game theoretic problem formulation and solution approach based on the new framework of distributed approachability and the study of the convergence properties of the resulting game model approachability theory is the theory of two player repeated games with vector payoffs and distributed approachability is here presented for the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local information and interaction structure the game model turns into a nonlinear differential inclusion which after a proper design of the control and disturbance policies presents a consensus term and an exogenous adversarial input local interactions enter into the model through a graph topology and the corresponding graph laplacian matrix given the above model we turn the original questions on cooperation competition and local interactions into convergence properties of the differential inclusion in particular we prove convergence and exponential convergence conditions around zero under general markovian strategies we illustrate our results in the case of decentralized organizations with multiple decision makers

nonlinear regulation in constrained input discrete time linear systems the use of composite linear and non linear feedback laws for the control of constrained input discrete time linear systems is re examined by making use of the delta operator formulation of a discrete time system an apparent restriction on the magnitude of the non linear control law is removed and the similarities between the continuous and discrete time solutions to the problem are elucidated in order to develop the results unconstrained systems are treated initially but it is shown that locally the sufficient conditions for the stabilization of such systems are actually equivalent to those for the stabilization of the corresponding constrained systems

brief paper stability and stabilization of discrete time periodic linear systems with actuator saturation this paper is concerned with the problems of stability and stabilization for discrete time periodic linear systems subject to input saturation both local results and global results are obtained for local stability and stabilization the so called periodic invariant set is used to estimate the domain of attraction the conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities lmis which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers the periodic enhancement technique is introduced to reduce the conservatism in the methods as a by product less conservative results for controller analysis and design for discrete time time invariant systems with input saturation are obtained for global stability by utilizing the special properties of the saturation function a saturation dependent periodic lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system the corresponding conditions are expressed in the form of lmis and can be efficiently solved several numerical and practical examples are given to illustrate the theoretical results proposed in the paper

hamiltonian mechanics of complex fluids constitutive relations for complex fluids e g polymeric fluids are derived from the assumption that the equations that govern the time evolution of the complex fluids possess the generalised hamiltonian structure the constitutive relations consist of a configuration space kinetic equation an extended local equilibrium relation an expression for the extra stress tensor and an expression for the heat flux in the particularly interesting case of complex fluids with spatially inhomogeneous internal structure the extra stress tensor includes an extension of the eriksen stress and the heat flux includes non fourier type contributions

robust control of multi input periodic discrete time systems with saturating actuators this paper proposes the use of a time varying sliding surface for robust transient shaping of periodic linear discrete time plants subject to saturating actuators in the presence of bounded matched uncertainties a constructive procedure is presented and ultimate boundedness of state trajectories is proved

the hamiltonian structure of the maxwell vlasov equations morrison 25 has observed that the maxwell vlasov and poisson vlasov equations for a collisionless plasma can be written in hamiltonian form relative to a certain poisson bracket we derive another poisson structure for these equations by using general methods of symplectic geometry the main ingredients in our construction are the symplectic structure on the co adjoint orbits for the group of canonical transformations and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory our poisson bracket satisfies the jacobi identity whereas morrison s does not 37 our construction also shows where canonical variables can be found and can be applied to the yang mills vlasov equations and to electromagnetic fluid dynamics

noncanonical poisson brackets for elastic and micromorphic solids this paper investigates the lagrangian to eulerian transformation approach to the construction of noncanonical poisson brackets for the conservative part of elastic solids and micromorphic elastic solids the dirac delta function links lagrangian canonical variables and eulerian state variables producing noncanonical poisson brackets from the corresponding canonical brackets specifying the hamiltonian functionals generates the evolution equations for these state variables from the poisson brackets different elastic strain tensors such as the green deformation tensor the cauchy deformation tensor and the higher order deformation tensor are appropriate state variables in poisson bracket formalism since they are quantities composed of the deformation gradient this paper also considers deformable directors to comprise the three elastic strain density measures for micromorphic solids furthermore the technique of variable transformation is also discussed when a state variable is not conserved along with the motion of the body

brief stability analysis of discrete time systems with actuator saturation by a saturation dependent lyapunov function in this paper stability of discrete time linear systems subject to actuator saturation is analyzed using a saturation dependent lyapunov function this saturation dependent lyapunov function captures the real time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction which is based on the solution of an lmi optimization problem numerical examples are presented to show the effectiveness of the proposed method

a complete characterization of the maximal contractively invariant ellipsoids of linear systems under saturated linear feedback as level sets of quadratic lyapunov functions ellipsoids have been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback for a linear system with a single input subject to actuator saturation based on a convex hull representation of saturation functions a necessary and sufficient condition for an ellipsoid to be contractively invariant was previously established which through the solution of an lmi problem leads to the maximal ellipsoidal invariant set in this technical note for a linear system with multiple inputs subject to actuator saturation we develop a complete characterization of the maximal ellipsoidal invariant set by algebraic computation simulation results demonstrate the effectiveness of our results

the differentiable structure of three remarkable diffeomorphism groups the goal of this paper is to find the lie groups for three well known lie algebras the globally hamiltonian vector fields the infinitesimal quantomorphisms and the homogeneous real valued functions of degree one on the cotangent bundle minus the zero section in all our considerations the underlying manifold is assumed to be compact without boundary before explaining and motivating our results a very brief review of the lie group structure of diffeomorphism groups is in order 9 10 18 if m n are compact boundaryless finite dimensional manifolds rn tn n the tangent bundle of n an hs map s dimm 2 from m to n has by definition all derivatives of order dim m 2 then the space ip m n of all such maps is a hilbert manifold whose tangent space at every point is the hilbert space t i h m n gelid m tn i n g f if e m is a vector bundle the same construction works for all hs sections hs e of e s dim m 2 if n ir hs m n will be denoted by c m ir let i m denote the diffeomorphisms of m of sobolev class h s l i e r t l m if and only if t is bijective and t t l m m are of class h 1 s l m is a topological group and since it is open in hs i m m it is also a hilbert manifold right multiplication r m i m r o t is c for each t y m and if t e s k l m left multiplication l t m i m l t o is c k the inversion map t t 1 in t m is only continuous the tangent maps of r and l at e the identity of a m are given by tr tel x t ox where x yys i m hs i tm the set of all h l vector fields on m the tangent space at e tr coincides with y m which is a sobolev space the bracket x y of x y f s i m is however only of class h one derivative is lost the usual bracket of vector fields is the lie algebra bracket of 5f x m i e if j

design of minimum phase digital filters as the sum of two allpass functions using the cepstrum technique a new and practical approach using the cepstrum technique is proposed in the design of minimum phase digital filters as the sum of two allpass functions the desired magnitude response is specified in the frequency domain its corresponding minimum phase response is then obtained from the desired magnitude response the desired phases for the two allpass filters are obtained from the magnitude and phase responses for both filters to be stable the corresponding denominator polynomials are minimum phase the filter coefficients are obtained from the desired phases using the cepstrum technique design examples show that the method works well for both classical filter specification and general magnitude specification in the frequency domain

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

exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation we present a necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under a saturated linear feedback the condition is given in terms of linear matrix inequalities lmis and can be easily used for optimization based analysis and design

taking into account period variations and actuators saturation in sampled data systems this paper deals with the problem of stability and stabilization of sampled data systems under asynchronous samplings and actuators saturation the method is based on the first hand on the use of a novel class of lyapunov functionals whose derivative is negative along the trajectories of the continuous time model of the sampled data system it is shown that this fact guarantees that a quadratic lyapunov function is strictly decreasing for the discrete time asynchronous system on the other side the control saturation is taken into account from the use of a modified sector condition these ingredients lead to the formulation of improved lmi conditions that can be cast in optimization problems aiming at enlarging estimates of the region of attraction of the closed loop system or maximizing the bounds on the sampling period jitter for which stability and stabilization are ensured

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

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

a simple example for comparing generic with rational non equilibrium thermodynamics during the last 15 years a bracket formalism of dissipative continuum physics has been developed which resulted in a formulation which is shortly denoted as generic generic has been applied to different problems of continuum thermodynamics often in this way that a well known problem was reformulated in generic formalism to learn some more about the generic procedure we consider a gas which is contained in a cylinder closed by a piston moving with friction we treat this simple discrete system with rational non equilibrium thermodynamics by using liu s procedure and for comparison also with the generic formalism both different procedures yield in the same results especially in the same entropy production differences similarities and fundamental presuppositions of both formalisms are discussed and compared

brief paper an improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation this paper is concerned with the treatment of saturation nonlinearity existing commonly in practical control systems an improved treatment of such nonlinearity is proposed which includes the well known linear differential inclusion method for handling saturation nonlinearity as a special case to show the effectiveness of this new treatment the problem of analysis and design of linear systems subject to nested saturation function is revisited the proposed results not only complement the existing work on this problem but also are less conservative than the existing methods four numerical examples are worked out to illustrate the applicability of the established approaches

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

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

robust control of uncertain multi inventory systems via linear matrix inequality we consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes we address the problem of e stabilising the inventory since this implies some reduction of the inventory costs the main results are certain conditions under which e stabilisability is possible through a saturated linear state feedback control all the results are based on a linear matrix inequalities approach and on some recent techniques for the modelling and analysis of polytopic systems with saturations numerical simulations are provided

non canonical poisson bracket for nonlinear elasticity with extensions to viscoelasticity the authors introduce a generalized bracket which is capable of generating the dynamical equations governing the flow of both elastic and viscoelastic media this generalized bracket is divided into two parts a noncanonical poisson bracket and a new dissipation bracket the non canonical poisson bracket is the eulerian equivalent of the canonical lagrangian poisson bracket corresponding to an ideal non dissipative continuum it is derived for a nonlinear elastic medium and then it is used to obtain the eulerian equations of motion in nonlinear elasticity valid for large deformations it is shown that the proposed non canonical bracket naturally leads to a materially objective relation involving the upper convected time derivative of a strain tensor as suggested by oldroyd 40 years ago the dissipation bracket for linear irreversible thermodynamics is next proposed in a general phenomenological circumstance so that the dissipation processes occurring in real systems viscous and relaxation phenomena can be incorporated into the hamiltonian formalism this bracket diverges from previously proposed dissipation brackets in that it uses the same generating functional i e the hamiltonian as the poisson bracket rather than an entropy functional or a dissipative potential it is shown that in combination with the choice of an appropriate hamiltonian functional the generalized bracket proposed here can generate the governing equations for many viscoelastic media including the voigt solid and the maxwell viscoelastic fluid

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

output feedback stabilization of linear systems with actuator saturation the note presents a method for designing an output feedback law that stabilizes a linear system subject to actuator saturation with a large domain of attraction this method applies to general linear systems including strictly unstable ones a nonlinear output feedback controller is first expressed in the form of a quasi lpv system conditions under which the closed loop system is locally asymptotically stable are then established in terms of the coefficient matrices of the controller the design of the controller coefficient matrices that maximizes an estimate of the domain of attraction is then formulated and solved as an optimization problem with lmi constraints

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

a partial differential equation with infinitely many periodic orbits chaotic oscillations of a forced beam this paper delineates a class of time periodically perturved evolution equations in a banach space whose associated poincar e map contains a smale horseshoe this implies that such systems possess periodic orbits with arbitrarily high period the method uses techniques originally due to melnikov and applies to systems of the form x f0 x f1 x t where x f0 x is hamiltonian and has a homoclinic orbit we give an example from structural mechanics sinusoidally forced vibrations of a buckled beam

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

improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback ellipsoids as level sets of quadratic lyapunov functions and the convex hull of ellipsoids as a level set of a certain composite quadratic lyapunov function have both been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback by expressing the saturated linear feedback law on the convex hull of a group of linear feedback laws which in turn expresses the linear system under this saturated linear feedback in a linear differential inclusion conditions have been established under which an ellipsoid or the convex hull of a group of ellipsoids are contractively invariant sets and are thus estimates of the domain of attraction these conditions are usually less conservative for single input systems than for multiple input systems in this paper we consider multiple input systems and establish conditions for contractive invariance of the convex hull of ellipsoids that are less conservative than the existing conditions

the maximal contractively invariant ellipsoids for discrete time linear systems under saturated linear feedback abstract in this paper we consider the problem of determining the maximal contractively invariant ellipsoids for discrete time linear systems with multiple inputs under saturated linear feedback we propose an algebraic computational approach to determining such maximal contractively invariant ellipsoids we divide the state space into several regions according to the saturation status of each input and compute the possible maximal contractively invariant ellipsoids on each region except the region where none of inputs saturate and on their intersections the minimal one among these possible maximal contractively invariant ellipsoids is the maximal contractively invariant ellipsoids of the system simulation results demonstrate the effectiveness of our methods

piecewise linear lq control for systems with input constraints abstract a piecewise linear control plc law based on lq theory is derived ths law raises an lq gain as the controlled error converges towards the origin it can be computed off line and it guarantees that input bounds are never exceeded without causing input saturation a succession of positively invariant sets are defined of diminishing size and associated with each is the corresponding highest lq gain possible in the presence of the input bounds the formulation gives rise to an iteration function whose solution is a fixed point fp the fp defines the optimal gain and the invariant set which comprise ellipsoids fp existence uniqueness and convergence properties are proven we explain the algorithms for the generation and subsequent implementation of the plc law the notion of a switching function is introduced consideration is given to the computational aspects of the fp the plc scheme is demonstrated for the linearized dynamics of the simple pendulum and the puma 560 robot a discrete time plc law can also be derived using the discrete time algebraic riccati equation

robust controller design of uncertain discrete time delay systems with input saturation and disturbances this technical note deals with the problem of robust controller design of uncertain discrete time delay systems subject to control input saturation and bounded external disturbances a sufficient condition is obtained which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain an iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers a simulation example is provided to demonstrate the effectiveness of the proposed method

poisson brackets and clebsch representations for magnetohydrodynamics multifluid plasmas and elasticity abstract poisson brackets are constructed by the same mathematical procedure for three physical theories ideal magnetohydrodynamics multifluid plasmas and elasticity each of these brackets is given a simple lie algebraic interpretation moreover each bracket is induced to physical space by use of a canonical poisson bracket in the space of clebsch potentials which are constructed for each physical theory by the standard procedure of constrained lagrangians

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

control of linear systems subject to time domain constraints with polynomial pole placement and lmis this note focuses on the control of continuous time linear systems subject to time domain constraints input amplitude limitation output overshoot on closed loop signals using recent results on positive polynomials it is shown that finding a youla kuc spl breve era polynomial parameter of fixed degree hence a controller of fixed order such that time domain constraints are satisfied amounts to solving a convex linear matrix inequality lmi optimization problem as soon as distinct strictly negative closed loop poles are assigned by pole placement proceeding this way time domain constraints are handled by an appropriate choice of the closed loop zeros

discrete time l and l2 norm vanishment and low gain feedback with their applications in constrained control the existing low gain feedback which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has been designed in very specific ways in this paper by recognizing the l and l 2 slow peaking phenomenon that exists in discrete time systems under low gain feedback more general notions of l and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals low gain feedback that does not lead to l and l 2 slow peaking in the control input are respectively referred to as l and l 2 low gain feedback based on the notions of l and l 2 vanishment not only can the existing low gain feedback be recognized as an l low gain feedback but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete time linear systems parallel to the effectiveness of l low gain feedback in magnitude constrained control the l 2 low gain feedback is instrumental in the control of discrete time systems with control energy constraints the notions of l and l 2 vanishment also result in a systematic approach to the design of l and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods

global stabilization with low computational cost of the discrete time chain of integrators by means of bounded controls this note proposes a bounded nonlinear control law composed of saturation functions for the discrete time chain of integrators a dynamical adaptation rule of the saturation levels involved in the control law is proposed to improve the closed loop performances the note unifies the original work of yang 1997 with static saturation level and convergence improvements that recently appeared in the continuous time case the possible ranges for the controller s parameters are extended with respect to existing results

a new approach to the realization of low sensitivity iir digital filters a new implementation of an iir digital filter transfer function is presented that is structurally passive and hence has extremely low pass band sensitivity the structure is based on a simple parallel interconnection of two all pass sections with each section implemented in a structurally lossless manner the structure shares a number of properties in common with wave lattice digital filters computer simulation results verifying the low sensitivity feature are included along with results on roundoff noise dynamic range interaction a large number of alternatives is available for the implementation of the all pass sections giving rise to the well known wave lattice digital filters as a specific instance of the implementation

on improving transient performance in global control of multiple integrators system by bounded feedback abstract the global stabilization problem for multiple integrators systems by bounded control is considered two classes of nonlinear feedback laws are proposed the first one consisting of nested saturation functions is a modification and generalization of that in a r teel global stabilization and restricted tracking for multiple integrators with bounded controls systems control letters 18 3 1992 165 171 and the other one consists of parallel connections of saturation functions both these two types of nonlinear feedback laws need only n n n 2 if n is even and n n 1 2 if n is odd where n is the length of the multiple integrators saturation elements furthermore the poles of the closed loop system can be placed on any location of the left real axis when none of the saturation elements in the control laws is saturated both of them exhibit simpler structure can significantly improve the transient performance of the closed loop system and are very superior to the other existing methods simulation of a fourth order system is used to illustrate the effectiveness of the proposed methods

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993

approximation and monotonicity of the maximal invariant ellipsoid for discrete time systems by bounded controls an analytic approximation of the maximal invariant ellipsoid for a discrete time linear system with bounded controls is derived the approximation is expressed explicitly in terms of the coefficient matrices of the system and the positive definite matrix that represents the shape of the invariant ellipsoid it is shown that this approximation is very close to the exact maximal invariant ellipsoid obtained by solving either an lmi based optimization problem or a nonlinear algebraic equation furthermore the necessary and sufficient condition for such an approximation to be equal to the exact maximal invariant ellipsoid is established on the other hand the monotonicity of the maximal invariant ellipsoid resulting from the minimal energy control with guaranteed convergence rate problem is established that shows a trade off between increasing the size of the invariant ellipsoid and increasing the convergence rate of the closed loop system under a bounded control two illustrative examples demonstrate of the effectiveness of the results

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