direct adaptive impedance control including transition phases this paper presents a new direct adaptive impedance controller for force position task that includes transition phases from free to constrained motions this scheme ensures global asymptotic stability without the need for a priori knowledge of environment stiffness one of the major consequence of this study is that a generalization of the time varying impedance leads to integral force feedback experimental results on a two degree of freedom planar manipulator are reported

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

observer design for unilaterally constrained lagrangian systems a passivity based approach this paper addresses the problem of state estimation in nonlinear lagrangian dynamical systems with frictionless unilateral constraints using the position measurement as output the discontinuous velocity variable in such systems is modeled as a function of bounded variation so that zeno phenomenon is not ruled out since the derivative of such functions is represented with the lebesgue stieltjes measure the framework of measure differential inclusions mdis is used to describe the dynamics a class of estimators is proposed which also uses the framework of mdis and is shown to generate asymptotically converging state estimates the existence and uniqueness of solutions for the proposed estimators is rigorously proven the global stability of error dynamics is analyzed using the generalized lyapunov methods for functions of bounded variation as particular cases of our estimators we provide an explicit construction of a full order observer and a reduced order observer

new limits to classical and quantum instance compression given an instance of a hard decision problem a limited goal is to compress that instance into a smaller equivalent instance of a second problem as one example consider the problem where given

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

brief new characterization and solution of input to state stabilization a state dependent scaling approach this paper proposes a novel approach to input to state stabilization and integral input to state stabilization problems for nonlinear systems based on the concept of state dependent scaling design both state feedback and output feedback controllers are constructed in a unified way the method provides global solutions whenever the system is in the strict feedback or output feedback form the paper allows the system to have structured static and dynamic uncertainties an advanced recursive procedure of observer design is the key to input to state stabilization by output feedback

on the tempered l functions conjecture we give a general proof of shahidi s tempered l function conjecture which has previously been known in all but one case one of the consequences is the standard module conjecture for p adic groups which means that the langlands quotient of a standard module is generic if and only if the standard module is irreducible and the inducing data generic we have also included the result that every generic tempered representation of a p adic group is a sub representation of a representation parabolically induced from a generic supercuspidal representation with a non negative real central character 1 introduction let f be a non archimedean local field of characteristic 0 let g be the group of points of a quasi split connected reductive f group by a parabolic subgroup borel subgroup levi subgroup torus split torus of g we will mean the group of points of an f parabolic subgroup f borel subgroup f levi subgroup f torus f split torus of the algebraic group under lying g fix a borel subgroup b tu of g a nd lett0 t be the maximal split torus in t i fm is any semi standard levi subgroup of g i e a levi subgroup which contains t0 a standard parabolic subgroup of m will be a parabolic subgroup of m which contains b m denote by w the weyl group of g defined with respect to t0 and by w g the longest element in w by sh3 section 3 we can fix a non degenerate character of u which for every levi subgroup m is compatible with w g 0 w m we will still denote by the restriction of to m u every generic representation of m becomes generic with respect to after changing the splitting in u let p mu be a standard parabolic subgroup of g and tm the maximal split torus in the center of m we will write a for the dual of the real lie algebra am of tm a c for its complexification and a m for the positive weyl chamber in a defined with respect to p following w we define a map hm m am such that m f q hm m for every f rational character a of m i f is a smooth representation of m and a c we denote by the smooth rep resentation of m defined by m q hm m m remark that although the sign in the definition of hm has been changed compared to the one due to harish chandra the meaning of is unchanged the symbol i g will denote the

on the standard modules conjecture let g be a quasi split p adic group under the assumption that the local coefficients c defined with respect to generic tempered representations of standard levi subgroups of g are regular in the negative weyl chamber we show that the standard module conjecture is true which means that the langlands quotient of a standard module is generic if and only if the standard module is irreducible

the linear quadratic regulator for periodic hybrid systems abstract the main objective of this paper is to characterize feedback control laws that are optimal with respect to a quadratic cost functional in the framework of linear hybrid systems undergoing time driven periodic jumps namely the so called hybrid linear quadratic regulator lqr problem the optimal solution to the hybrid lqr problem is determined both in the case of finite horizon and infinite horizon optimal control problems by introducing a hybrid periodic extension of the classic differential and difference riccati equations thus leading to the notion of monodromy riccati equation interestingly due to the periodic nature of the discrete time events the computation of the optimal feedback hinges upon the solution of a differential rather than algebraic riccati equation also in the infinite horizon case hence yielding a time varying periodic control law necessary and sufficient conditions that ensure asymptotic stability of the closed loop system are provided and discussed in detail in the case of infinite horizon optimal control problems

on robustness of finite time stability of homogeneous affine nonlinear systems and cascade interconnections this paper investigates robustness of finite time stability property for a homogeneous nonlinear dynamical system with sufficiently small affine inputs in addition robust stability conditions are presented for the systems admitting homogeneous approximations at the origin or at infinity the effects of additional stable unmodeled dynamics in the input channel on robust stability are investigated the utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time varying gains

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

global exponential observers for two classes of nonlinear systems abstract this paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems i the class of systems with a globally asymptotically stable compact set and ii the class of systems that evolve on an open set in the first class the derived continuous time observer also leads to the construction of a robust global sampled data exponential observer under additional conditions two illustrative examples of applications of the general results are presented one is a system with monotone nonlinearities and the other is a chemostat system

relaxing the conditions for parameter estimation based observers of nonlinear systems via signal injection parameter estimation based observers are a new kind of state reconstruction methods where the state observation task is translated into an on line parameter estimation problem a key step for its application is the transformation of the system dynamics into a particular cascade form which involves the solution of a partial differential equation that moreover should satisfy some injective requirement in this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks in this way we make this observer applicable to a wider class of nonlinear systems even with indistinguishable states the application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems

design of sliding observers for lipschitz nonlinear system using a new time averaged lyapunov function abstractthis paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of gaussian input disturbances and sensor noises the paper first proposes a nov

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

state and unknown input observers for nonlinear systems with bounded exogenous inputs a systematic design methodology for state observers for a large class of nonlinear systems with bounded exogenous inputs disturbance inputs and sensor noise is proposed the nonlinearities under consideration are characterized by an incremental quadratic constraint parameterized by a set of multiplier matrices linear matrix inequalities are developed to construct observer gains which ensure that a performance output based on the state estimation error satisfies a prescribed degree of accuracy furthermore conditions guaranteeing estimation of the unknown inputs to arbitrary degrees of accuracy are provided the proposed scheme is illustrated with a numerical example which does not satisfy the so called matching conditions

input to error stable observer for nonlinear sampled data systems with application to one sided lipschitz systems in this paper the design of sampled data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals we establish general design principles using the standard approaches of i direct discrete time design via approximation and ii discretization of a continuous time observer emulation by interpreting the disturbances as exogenous inputs affecting the error dynamics sufficient conditions are derived which ensure the input to state stability iss of the observer error system in a semiglobal practical sense for the unknown exact discrete time model next we focus on systems whose vector fields are one sided lipschitz to develop constructive design techniques via linear matrix inequalities lmis numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled data estimators

adaptive rejection of non linear disturbances in extended non linear output feedback systems this paper deals with asymptotic rejection of disturbances generated from non linear exosystems for uncertain nonlinear systems in an extended output feedback form which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements a new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance adaptive control techniques are then used to deal with the uncertainty in the system the proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables

on non linear unknown input observers applied to lateral vehicle velocity estimation on banked roads unknown input observers uios are observers that have stable error dynamics that are independent of unknown inputs this paper studies such observers for non linear systems and shows that the error dynamics for a non linear uio has the same structure as the error dynamics of a non linear observer without unknown inputs this result is first used to provide synthesis inequalities for uios for a class of non linear systems and secondly to inspire the design of an observer for estimation of vehicle lateral velocity on banked roads

jacquet modules and local langlands correspondence in this paper we explicitly compute the semisimplifications of all jacquet modules of irreducible representations with generic l parameters of p adic split odd special orthogonal groups or symplectic groups our computation represents them in terms of linear combinations of standard modules with rational coefficients the main ingredient of this computation is to apply m glin s explicit construction of local a packets to tempered l packets finally we study the derivatives introduced by minguez

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

list matrix partitions of chordal graphs it is well known that a clique with k 1 vertices is the only minimal obstruction to k colourability of chordal graphs a similar result is known for the existence of a cover by l cliques both of these problems are in fact partition problems restricted to chordal graphs the first seeks partitions into k independent sets and the second is equivalent to finding partitions into l cliques in an earlier paper we proved that a chordal graph can be partitioned into k independent sets and l cliques if and only if it does not contain an induced disjoint union of l 1 cliques of size k 1 a linear time algorithm for finding such partitions can be derived from the proof in this paper we expand our focus and consider more general partitions of chordal graphs for each symmetric matrix m over 0 1 the m partition problem seeks a partition of the input graph into independent sets cliques or arbitrary sets with certain pairs of sets being required to have no edges or to have all edges joining them as encoded in the matrix m moreover the vertices of the input chordal graph can be equipped with lists restricting the parts to which a vertex can be placed such list partitions generalize list colourings and list homomorphisms and arise frequently in the theory of graph perfection we show that many m partition problems that are np complete in general become solvable in polynomial time for chordal graphs even in the presence of lists on the other hand we show that there are m partition problems without lists that remain np complete for chordal graphs it is not known whether or not each list m partition problem is np complete or polynomial but it has been shown that each is np complete or quasi polynomial no log n for chordal graphs even this quasi dichotomy is not known but we do identify large families of matrices m for which dichotomy or at least quasi dichotomy holds we also discuss forbidden subgraph characterizations of graphs admitting an m partition such characterizations have recently been investigated for partitions of perfect graphs and we focus on highlighting the improvements one can obtain for the class of chordal rather than just perfect graphs

brief paper explicit construction of h control law for a class of nonminimum phase nonlinear systems this paper addresses a nonlinear h control problem for a class of nonminimum phase nonlinear systems the given system is first transformed into a special coordinate basis in which the system zero dynamics is divided into a stable part and an unstable part a sufficient solvability condition is then established for solving the nonlinear h control problem moreover based on the sufficient solvability condition an upper bound of the best achievable l 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear h control problem the proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear h control problem in particular the solution to the nonlinear h control problem does not require solving any hamilton jacobi equations finally the obtained results are utilized to solve a benchmark problem on a rotational translational actuator rtac system

the gross prasad conjecture and local theta correspondence we establish the fourier jacobi case of the local gross prasad conjecture for unitary groups by using local theta correspondence to relate the fourier jacobi case with the bessel case established by beuzart plessis to achieve this we prove two conjectures of prasad on the precise description of the local theta correspondence for almost equal rank unitary dual pairs in terms of the local langlands correspondence the proof uses arthur s multiplicity formula and thus is one of the first examples of a concrete application of this global reciprocity law

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

velocity observers for linear mechanical systems subject to single non smooth impacts abstract in this paper we consider the problem of the velocity estimation from position measurement for linear mechanical systems with multiple degrees of freedom subject to single non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively through a simple example it is shown that a classical luenberger observer is not able to reproduce instantaneously the jumps in the mass velocities since it recovers the error induced by such jumps only asymptotically an infinite sequence of impacts can prevent the estimation error to asymptotically go to zero a new observer structure is proposed for linear mechanical systems subject to single unilateral constraints that guarantees that the corresponding error dynamics are exponentially stable also in presence of an infinite sequence of non smooth impacts the observer that we propose switches at the impact times that can be recognized by position measurements only to validate the proposed observer both simulation and experimental tests have been carried out and are briefly reported pointing out the drawbacks and advantages of the observer

a note on non linear observers a general non linear exponential observer is presented for non linearly perturbed nonlinear systems this is done by using the non linear variation of constants formula

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

adaptive redesign of nonlinear observers to estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers in this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented the redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties to enable parameter adaption a new type of update law is derived using lyapunov analysis and a nonlinear coordinate transformation the uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states and still achieves convergence of the state estimate without requiring persistent excitation two examples are presented that demonstrate these properties

hybrid output regulation for linear systems with periodic jumps solvability conditions structural implications and semi classical solutions the problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper necessary and sufficient conditions for its solution are provided both in the full information and error feedback case by a detailed analysis of such conditions several interesting properties are derived including the fact that the regulator must contain a suitably defined copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics and the fact that the output regulation problem is generically solvable for fat plants having more inputs than outputs and generically not solvable for square plants in addition semi classical solutions to the hybrid output regulation problem are introduced and discussed such solutions are characterized by the property that the required steady state input can be generated as a simple linear function of the state of the exosystem as in the non hybrid case although the associated steady state response has a genuinely hybrid structure

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

robust output feedback guaranteed cost control of nonlinear stochastic uncertain systems via an iqc approach this technical note presents a new approach to constructive output feedback robust nonlinear controller design based on the use of iqcs and minimax lqg control the approach involves a class of controllers which include copies of the nonlinearities in the controller the linear part of the controller is synthesized using minimax lqg control theory which is closely related to h infin control theory

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

on the control of finite dimensional mechanical systems with unilateral constraints this paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees of freedom subject to unilateral constraints on the position roughly speaking those systems are described by a set of ordinary differential equations that represent smooth dynamics together with an algebraic inequality condition f q spl ges 0 where q is the vector of generalized coordinates and an impact rule relating the interaction impulse and the velocity nonsmooth dynamics is at the core of the study of such systems this implies that one can suitably define solutions and stability concepts that fit with the considered model we then discuss the closed loop control problem and analyze various switching control strategies

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

high gain observer for a class of non triangular systems this paper presents a high gain observer for a class of mimo nonlinear systems involving some uncertainties the latter is particularly composed of cascade subsystems where each subsystem is associated with a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems the main contribution consists in extending the available results to allow more interconnections between the subsystems of fundamental interest it is shown that the underlying observation error exponentially converges to zero in the absence of uncertainties moreover the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

modeling and control of impact in mechanical systems theory and experimental results considers the equations of motion of mechanical systems subject to inequality constraints which can be obtained by looking for the stationary value of the action integral two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral the valentine variables method and the penalty functions method the equations of motion resulting from the application of the valentine variables method which introduces the concept of nonsmooth impacts constitute the exact model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff the equations of motion resulting from the application of the penalty functions method which introduces the concept of smooth impacts constitute an approximate model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact the closed loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties the proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment the effectiveness of the proposed control structure has been tested experimentally with reference to a single link robot arm showing a valuable behavior

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

structural properties of a class of linear hybrid systems and output feedback stabilization in this paper we deal with the problem of output feedback stabilization for a class of linear hybrid systems this problem is addressed by characterizing the structural properties of such a class of systems namely reachability controllability stabilizability observability constructibility and detectability are framed in terms of algebraic and geometric conditions on the data of the system two canonical forms recalling the classical kalman decompositions with respect to reachability and observability are given by taking advantage of this characterization duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time invariant output feedback compensator are stated compared with previous results no assumption is needed on the plant about minimum phaseness relative degree or squareness

kazhdan lusztig representations and whittaker space of some genuine representations we prove a formula for the dimension of whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups the formula explicitly relates such dimension to the kazhdan lusztig representations associated with certain right cells of the weyl group we also state a refined version of the formula which is proved under some natural assumption the refined formula is also verified unconditionally in several important cases

brief paper global nonlinear output regulation convergence based controller design in this paper we present output feedback controllers solving the global output regulation problem for a class of nonlinear systems the proposed controllers are based on the notion of convergent systems the presented solution extends well established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case for lur e systems which are not necessarily in the output feedback form the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities for systems in the output feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system which is crucial in the previous regulator designs for output feedback systems the results are illustrated by examples

velocity observers for non linear mechanical systems subject to non smooth impacts this paper is concerned with the estimation of the velocity variables when the position variables are the measured outputs for non linear mechanical systems subject to non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively a reduced order observer is proposed which guarantees that the corresponding error system despite the possible presence of an infinite sequence of non smooth impacts is locally exponentially stable an estimate of the basin of attraction is also given

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

on the parameterized complexity of recognizing well covered r l graph an r ell partition of a graph g is a partition of its vertex set into r independent sets and ell cliques a graph is r ell if it admits an r ell partition a graph is well covered if every maximal independent set is also maximum a graph is r ell well covered if it is both r ell and well covered in this paper we consider two different decision problems in the r ell well covered graph problem r ell wcg for short we are given a graph g and the question is whether g is an r ell well covered graph in the well covered r ell graph problem wc r ell g for short we are given an r ell graph g together with an r ell partition of v g into r independent sets and ell cliques and the question is whether g is well covered we classify most of these problems into p conp complete np complete np hard or conp hard only the cases wc r 0 g for r ge 3 remain open in addition we consider the parameterized complexity of these problems for several choices of parameters such as the size alpha of a maximum independent set of the input graph its neighborhood diversity or the number ell of cliques in an r ell partition in particular we show that the parameterized problem of deciding whether a general graph is well covered parameterized by alpha can be reduced to the wc 0 ell g problem parameterized by ell and we prove that this latter problem is in xp but does not admit polynomial kernels unless mathsf conp subseteq mathsf np mathsf poly

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

certainty equivalence output feedback design with circle criterion observers we study how the class of observers introduced in a previous paper here referred to as circle criterion observers can be incorporated in output feedback control due to the absence of a controller observer separation property for nonlinear systems the certainty equivalence implementation of a state feedback design may lead to severe forms of instability we show on the contrary that the state dependent convergence properties of circle criterion observers can prevent such instabilities exploiting these convergence properties we develop a modified circle criterion observer design that guarantees global asymptotic stability for certainty equivalence controllers

robust nonlinear observer for lipschitz nonlinear systems subject to disturbances this note proposes a robust nonlinear observer for systems with lipschitz nonlinearity the proposed nonlinear observer whose linear part adopts the linear ltr observer design technique has two important advantages over previous designs first the new observer does not impose the small lipschitz constant condition on the system nonlinearity nor other structural conditions on the system dynamics as in the existing observer designs second it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

absolute stability of second order systems with asymmetric sector boundaries absolute stability is considered under an asymmetric sector condition resulting in a generalization of the classical absolute stability analysis in addition to the extension to asymmetric sector conditions the current approach based on the recent work of leonov 2005 yields results that are both necessary and sufficient for absolute stability an asymmetric sector condition allows different sector bounds to be imposed in different regions of the state space and removes the restriction that the system nonlinearity be confined to only the first and third quadrants this work applies to second order systems the necessary and sufficient conditions are derived by comparing the vector field of the nonlinear system with that of certain piecewise linear systems as an example stabilization of a supercavitating underwater vehicle system is considered and it is shown that the new results are less conservative than those obtained with classical theory which requires imposition of a symmetric sector condition

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example