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

irreducible embeddings and polynomial tensors the problem of finding irreducible tensors which are polynomials in the components of an irreducible tensor n of a compact semisimple group h is simplified if the representation n is contained irreducibly in a representation m of a larger group g of which h is a subgroup a number of examples are given for which the problem is completely solved by generating function methods the authors discuss how one can use the computer to tackle the more difficult cases the problem of the reduction of the so 8 enveloping algebra is given as an example

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

fast recursion formula for weight multiplicities the purpose of this note is to describe and prove a fast recursion formula for computing multiplicities of weights of finite dimensional representations of simple lie algebras over c until now information about weight multiplicities for all but some special cases 1 2 has had to be found from the recursion formulas of freudenthal 3 or racah 4 typically these formulas become too laborious to use for hand computations for ranks 5 and dimensions 1 0 0 and for ranks 10 and dimensions 10 on a large computer 5 6 with the proposed method the multiplicities can routinely be calculated even by hand for dimensions far exceeding these as an example we present a summary of calculations 7 of all multiplicities in the first sixteen irreducible representations of es let be a semisimple lie algebra over c with root system a and weyl group w relative to a cartan subalgebra let a be the positive roots with respect to some ordering and ii at a the set of simple roots let q and p be the root and weight lattices respectively spanning the real vector space f c if x c p we denote by x the set of dominant elements of x relative to n let m be an irreducible module with highest weight a and weight system 2 an important feature of the approach is the direct determination of 2 without computing outside the dominant chamber since every w orbit is represented by one weight x 2 of the same multiplicity it suffices to compute such x s the recursion formula for computing the multiplicities is a modification proposition 4 of the freudenthal formula in which the weyl group has been exploited to collapse it as much as possible after describing the procedure we present the e example finally the necessary proofs are given

su n and sp 2n wzw fusion rules fusion rules for wzw models based on su n and sp 2n are considered using the results of kac 1989 and walton 1989 1990 it is shown that these fusion rules may be computed using young diagram methods by performing extra modifications these modifications take the form of the removal of boundary strips which bear a striking resemblance to the modifications necessary when performing tensor products for these algebras this fact is exploited to exhibit a duality between the fusion rules of su n at level k and su k at level n and also between sp 2n at level k and so 2k at level n the former duality has been discussed in the context of two dimensional statistical mechanics by kuniba and nakanishi 1990 and also by naculich and schnitzer 1990 in the case of wzw models and goodman and wenzl 1989 for hecke algebras at roots of unity for su 3 a manifestly positive combinatorial procedure for computing fusion rules and a generating function for the fusion coefficients are given

alternative descriptions and bipartite compound quantum systems we analyse some features of alternative hermitian and quasi hermitian quantum descriptions of simple and bipartite compound systems we show that alternative descriptions of two interacting subsystems are possible if and only if the metric operator of the compound system can be obtained as a tensor product of positive operators on component spaces some examples also show that such property could be strictly connected with symmetry properties of the non hermitian hamiltonian

simple wzw currents a complete classification of simple currents of wzw theories is obtained the proof is based on an analysis of the quantum dimensions of the primary fields simple currents are precisely the primaries with unit quantum dimension for wzw theories explicit formulae for the quantum dimensions can be derived so that an identification of the fields with unit quantum dimension is possible

lie group weight multiplicities from conformal field theory dominant weight multiplicities of simple lie groups are expressed in terms of the modular matrices of wess zumino witten conformal field theories and related objects symmetries of the modular matrices give rise to new relations among multiplicities at least for some lie groups these new relations are strong enough to completely fix all multiplicities

reduction of orbits of finite coxeter groups of non crystallographic type a reduction of orbits of finite reflection groups to their reflection subgroups is produced by means of projection matrices which transform points of the orbit of any group into points of the orbits of its subgroup projection matrices and branching rules for orbits of finite coxeter groups of non crystallographic type are presented the novelty in this paper is producing the branching rules that involve non crystallographic coxeter groups moreover these branching rules are relevant to any application of non crystallographic coxeter groups including molecular crystallography and encryption

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 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

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

computation of character decompositions of class functions on compact semisimple lie groups a new algorithm is described for splitting class functions of an arbitrary semisimple compact lie group k into sums of irreducible characters the method is based on the use of elements of finite order efo in k and is applicable to a number of problems including decompositions of tensor products and various symmetry classes of tensors as well as branching rules in group subgroup reductions the main feature is the construction of a decomposition matrix d computed once and for all for a given range of problems and for a given k which then reduces any particular splitting to a simple matrix multiplication determination of d requires selection of a suitable set s of conjugacy classes of efo representing a finite subgroup of a maximal torus t of k and the evaluation of weyl group orbit sums on s in fact the evaluation of d can be coupled with the evaluation of the orbit sums in such a way as to greatly enhance the efficiency of the latter the use of the method is illustrated by some extensive examples of tensor product decompositions in e6 modular arithmetic allows all computations to be performed exactly

algebraic equations determining quantum dimensions we show that a quantum dimension dq lambda for a representation rho of uq g a quantized universal enveloping algebra of a compact and simple lie group g is computed from the algebraic equations which we found recently in studying 2 1 dimensional chern simons theory we solve the equations explicitly for the typical examples of all compact and simple lie groups this method can be applied to super lie groups such as su m n and osp m n

subjoinings of affine kac moody algebras subjoinings among affine kac moody algebras is a relation generalising the algebra subalgebra relation it is analogous to subjoinings among semisimple finite lie algebras a list of maximal subjoinings of equal rank affine kac moody algebras is presented it is conjectured that there are no other maximal subjoinings

an antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation the article considers linear systems subject to actuator saturation an antiwindup technique is used to enlarge the domain of attraction of the closed loop system under an a priori designed linear dynamic feedback law the design of the antiwindup compensation gain is formulated and solved as an iterative optimization problem with lmi constraints numerical examples are used to demonstrate the effectiveness of the proposed design technique

recursion relations and branching rules for simple lie algebras the branching rules between simple lie algebras and their regular maximal simple subalgebras are studied two types of recursion relations for anomalous relative multiplicities are obtained one of them is proved to be the factorized version of the other the factorization property is based on the existence of the set of weights specific for each injection the structure of is easily deduced from the correspondence between the root systems of the algebra and subalgebra the recursion relations thus obtained give rise to a simple and effective algorithm for branching rules the details are illustrated by performing the explicit decomposition procedure for the injection

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

some symmetries of quantum dimensions several useful properties of the quantum dimensions of representations of uq sl n for q a root of unity are established the results can be used to calculate truncated kronecker products of these representations and hence to investigate the isomorphism between these truncated tensor products and the fusion rules of the wzw theories associated with uq sl n

exact pt symmetry is equivalent to hermiticity we show that a quantum system possessing an exact antilinear symmetry in particular pt symmetry is equivalent to a quantum system having a hermitian hamiltonian we construct the unitary operator relating an arbitrary non hermitian hamiltonian with exact pt symmetry to a hermitian hamiltonian we apply our general results to pt symmetry in finite dimensions and give the explicit form of the above mentioned unitary operator and hermitian hamiltonian in two dimensions our findings lead to the conjecture that non hermitian cpt symmetric field theories are equivalent to certain nonlocal hermitian field theories

orbit orbit branching rules between simple low rank algebras and equal rank subalgebras complete orbit orbit branching rules or equivalently reduction of weyl group orbits between each simple algebra of rank 3 or less and its equal rank subalgebras and between f4 and each of its equal rank subalgebras are given the generic case an an 1 u 1 the subjoining f4 b3 u 1 and e8 e6 a2 first and seventh highest weight labels nonzero are also treated branching rules between rank 4 and 5 simple algebras and e6 and their equal rank subalgebras are available in a depository

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

pt symmetric cubic anharmonic oscillator as a physical model there is a factor of 2 error in equation 61 of this paper correcting this error leads to minor changes in equations 62 and 63 please see pdf for details

some invariant biorthogonal sets with an application to coherent states abstract we show how to construct out of a certain basis invariant under the action of one or more unitary operators a second biorthogonal set with similar properties in particular we discuss conditions for this new set to be also a basis of the hilbert space and we apply the procedure to coherent states we conclude the paper considering a simple application of our construction to pseudo hermitian quantum mechanics

orbit orbit branching rules for families of classical lie algebra subalgebra pairs complete orbit orbit branching rules are derived for each classical algebra maximal subalgebra pair cm ncm cn bm ndm bn dm ndm dn since each pair is equal rank and algebra and subalgebra weyl sectors line up the integrity basis in each case consists of the subalgebra orbits contained in the fundamental orbits of the algebra

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

the demazure tits subgroup of a simple lie group the demazure tits subgroup of a simple lie group g is the group of invariance of clebsch gordan coefficients tables assuming an appropriate choice of basis the structure of the demazure tits subgroups of an bn cn dn and g2 is described orbits of the permutation action of the dt group in any irreducible finite dimensional representation space of a2 c2 and g2 are decomposed into the sum of irreducible representations of the dt group

polytope expansion of lie characters and applications the weight systems of finite dimensional representations of complex simple lie algebras exhibit patterns beyond weyl group symmetry these patterns occur because weight systems can be decomposed into lattice polytopes in a natural way since lattice polytopes are relatively simple this decomposition is useful in addition to being more economical than the decomposition into single weights an expansion of characters into polytope sums follows from the polytope decomposition of weight systems we study this polytope expansion here a new general formula is given for the polytope sums involved the combinatorics of the polytope expansion are analyzed we point out that they are reduced from those of the weyl character formula described by the kostant partition function in an optimal way we also show that the weight multiplicities can be found easily from the polytope multiplicities indicating explicitly the equivalence of the two descriptions finally we demonstrate the utility of the polytope expansion by showing how polytope multiplicities can be used in the calculation of tensor product decompositions and subalgebra branching rules

interactions of hermitian and non hermitian hamiltonians the coupling of non hermitian symmetric hamiltonians to standard hermitian hamiltonians each of which individually has a real energy spectrum is explored by means of a number of soluble models it is found that in all cases the energy remains real for small values of the coupling constant but becomes complex if the coupling becomes stronger than some critical value for a quadratic non hermitian symmetric hamiltonian coupled to an arbitrary real hermitian symmetric hamiltonian the reality of the ground state energy for small enough coupling constant is established up to second order in perturbation theory

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

meromorphic c 24 conformal field theories modular invariant conformal field theories with just one primary field and central charge c 24 are considered it has been shown previously that if the chiral algebra of such a theory contains spin 1 currents it is either the leech lattice cft or it contains a kac moody sub algebra with total central charge 24 in this paper all meromorphic modular invariant combinations of the allowed kac moody combinations are obtained the result suggests the existence of 71 meromorphic c 24 theories including the 41 that were already known

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

weyl orbits and their expansions in irreducible representations for affine kac moody algebras weyl orbits of affine rank 2 and 3 algebras are obtained analytically along with the depths of their weights in terms of an integrity basis consisting of sets of compatible or adjacent weights one from each fundamental orbit the fundamental orbits and others of the same level and congruence class are then decomposed into irreducible representations ir since the orbit ir matrix is triangular it will be easy to invert it to get orbit multiplicities and subalgebra branching rules

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 switching anti windup design based on partitioning of the input space abstract this paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti windup compensator the closed loop system consisting of the plant the controller and the anti windup compensator is first equivalently formulated as a linear system with input deadzone we then partition the input space into several regions in one of these regions all inputs saturate with the time derivative of the saturated input being zero in each of the remaining regions there is a unique input that does not saturate the time derivative of the deadzone function associated with the unsaturating input is zero by utilizing these special properties of the inputs on an existing piecewise lyapunov function of the augmented state vector containing the deadzone function of inputs we design a separate anti windup gain for each region of the input space the switching from one anti windup gain to another is activated when the input signals leave one region for another which can be implemented online since only the measurement of the input signals is required simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches

branching rules for representations of simple lie algebras through weyl group orbit reduction two independent algorithms are presented which together allow the determination of branching rules from an irreducible representation of a compact lie algebra to those of a subalgebra or subjoined algebra the first gives the subalgebra weyl orbits contained in an algebra orbit the second gives the irreducible representations of an algebra contained in an orbit and by inversion of a triangular matrix the orbits contained in an irreducible representation

complex wkb analysis of energy level degeneracies of non hermitian hamiltonians the hamiltonian h p 2 x 4 iax where a is a real parameter is investigated the spectrum of h is discrete and entirely real and positive for a 3 169 as a increases past this point adjacent pairs of energy levels coalesce and then become complex starting with the lowest lying energy levels for large energies the values of a at which this merging occurs scale as the three quarters power of the energy that is as a and e at the points of coalescence the ratio a a e 3 4 approaches a constant whose numerical value is acrit 1 1838363072914 conventional wkb theory determines the high lying energy levels but cannot be used to calculate acrit this critical value is predicted exactly by complex wkb theory

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

on exploring the domain of attraction for bilateral teleoperator subject to interval delay and saturated p d control scheme the domain of attraction problem is investigated for networked teleoperation system subject to actuator saturation the forward and backward time varying communication delays are assumed to be interval and asymmetric which is the case for network based teleoperation system we propose a novel lyapunov krasovskii functional for the closed loop teleoperation system with the consideration of the interval values of the time delays the delay dependent estimation of the domain of attraction is presented using linear matrix inequality lmi technique the problem of designing mathrm p mathrm d control law such that the domain of attraction is enlarged is formulated and solved as an optimization problem with lmi constraints experiments are performed to verify the effectiveness of the proposed approach

orbit orbit branching rules between classical simple lie algebras and maximal reductive subalgebras complete orbit orbit branching rules are found for the classical algebra maximal reductive subalgebra pairs am n 1 am an u 1 bm 1 bm u 1 cm 1 am u 1 dm 1 dm u 1 and dm 1 am u 1

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

transition elements for a non hermitian quadratic hamiltonian the non hermitian quadratic hamiltonian h a a a2 a 2 is analyzed where a and a are harmonic oscillator creation and annihilation operators and and are real constants for the case that 2 4 0 it is shown using operator techniques that the hamiltonian possesses real and positive eigenvalues a generalized bogoliubov transformation allows the energy eigenstates to be constructed from the algebra and states of the harmonic oscillator the eigenstates are shown to possess an imaginary norm for a large range of the parameter space finding the orthonormal dual space allows the inner product to be redefined using the complexification procedure of bender et al for non hermitian hamiltonians transition probabilities governed by h are shown to be manifestly unitary when the complexification procedure is followed a specific transition element between harmonic oscillator states is evaluated for both the hermitian and non hermitian cases to identify the differences in time evolution

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

anti windup strategies for discrete time switched systems subject to input saturation this paper deals with the design of anti windup compensator for discrete time switched systems subject to input saturation the cases of static and dynamic anti windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed loop system two aspects of the switching law are taken into account during the design either it is arbitrary or it is a part of the complete control law theoretical conditions allowing to synthesise the anti windup compensator are mainly described through linear matrix inequalities computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution

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

saturation based switching anti windup design for linear systems with nested input saturation this paper proposes a saturation based switching anti windup design for the enlargement of the domain of attraction of a linear system subject to nested saturation a nestedly saturated linear feedback is expressed as a linear combination of a set of auxiliary linear feedbacks which form a convex hull where the nestedly saturated linear feedback resides this set of auxiliary linear feedbacks is then partitioned into several subsets the auxiliary linear feedbacks in each of these subsets form a convex sub hull of the original convex hull when the value of the nestedly saturated linear feedback falls into a convex sub hull it can be expressed as a linear combination of the subset of all the auxiliary feedbacks that form the convex sub hull a separate anti windup gain is designed for each convex sub hull by using a common quadratic lyapunov function and is implemented when the value of the nestedly saturated linear feedback falls into this convex sub hull 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