necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

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

brief almost global stabilization of the inverted pendulum via continuous state feedback continuous state feedback laws are presented for almost global stabilization of the planar inverted pendulum on a cart the synthesis is carried out exploiting energy shaping techniques and a suitable smooth switching between positive and negative feedback some of the employed ideas could be possibly generalized to the problem of stabilization of systems with multiple equilibrium points

controlled lagrangians and the stabilization of mechanical systems ii potential shaping for pt i see ibid vol 45 p 2253 70 2000 we extend the method of controlled lagrangians cl to include potential shaping which achieves complete state space asymptotic stabilization of mechanical systems the cl method deals with mechanical systems with symmetry and provides symmetry preserving kinetic shaping and feedback controlled dissipation for state space stabilization in all but the symmetry variables potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables the approach also extends the method of controlled lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

energy control of a pendulum with quantized feedback the problem of controlling a nonlinear system to an invariant manifold using quantized state feedback is considered by the example of controlling the pendulum s energy a feedback control law based on the speed gradient algorithm is chosen the main result consisting in precisely characterizing allowed quantization error bounds and resulting energy deviation bounds is presented

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

lyapunov formulation of the large scale iss cyclic small gain theorem the discrete time case abstract this paper presents a lyapunov formulation of the cyclic small gain theorem for dynamical networks composed of discrete time input to state stable iss subsystems iss lyapunov functions for dynamical networks satisfying the cyclic small gain condition are constructed from the iss lyapunov functions of the subsystems

sufficient conditions for the stability of a class of second order systems this paper provides sufficient conditions to assess the stability and input to state stability of a class of second order systems by only looking at the structure of the dynamic equations these results are proven by using the variable gradient method to build suitable lyapunov functions the paper includes a number of relevant examples that highlight the value of the contribution

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

capacity of the l p norm constrained poisson channel the capacity of the poisson channel is derived with a specified constraint imposed on the lp norm t p of the encoder intensity formulae are given for the capacity which establish previously known results for p 1 p 2 and p to be part of a system of capacity problems with common form and solution these formulae apply with or without causal feedback and whether or not the encoder intensity is ook on off keying constrained

necessary and sufficient conditions for uniform semiglobal practical asymptotic stability application to cascaded systems it is well established that for a cascade of two uniformly globally asymptotically stable ugas systems the origin remains ugas provided that the solutions of the cascade are uniformly globally bounded while this result has met considerable popularity in specific applications it remains restrictive since in practice it is often the case that the decoupled subsystems are only uniformly semiglobally practically asymptotically stable uspas recently we established that the cascade of uspas systems is uspas under a local boundedness assumption and the hypothesis that one knows a lyapunov function for the driven subsystem the contribution of this paper is twofold 1 we present a converse theorem for uspas and 2 we establish uspas of cascaded systems without the requirement of a lyapunov function compared to other converse theorems in the literature ours has the advantage of guaranteeing a specific relationship between the upper and lower bounds on the generated lyapunov function v and of providing a time invariant bound on the gradient of v which is fundamental to establish theorems for cascades

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

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

a tight small gain theorem for not necessarily iss systems a new version of the small gain theorem is presented for nonlinear finite dimensional systems the result provides conditions for global asymptotic stability under relaxed assumptions in particular the two interconnected subsystems need not be input to state stable in open loop

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

lyapunov formulation of iss cyclic small gain in continuous time dynamical networks this paper provides a lyapunov formulation of the cyclic small gain theorem for general dynamical networks large scale systems composed of continuous time input to state stable iss subsystems iss lyapunov functions for continuous time dynamical networks satisfying cyclic small gain conditions are constructed from the iss lyapunov functions of the subsystems

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

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

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

rate limited time optimal control of a planar pendulum abstract time optimal control problems often admit as solution bang bang controls but they present several drawbacks in real applications where additional degrees of regularity are desirable in this paper the rate limited time optimal swing up of an inverted pendulum is considered and necessary conditions that have to be satisfied by optimal trajectories in the presence of rate constraints are derived a comparison between this approach and the results from the standard time optimal problem is reported

brief paper capability and limitation of max and sum type construction of lyapunov functions for networks of iiss systems this paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input to state stability iiss we focus on two ways of constructing a lyapunov function satisfying a dissipation inequality of a given network their difference from one another is elucidated from the viewpoint of formulation relation fundamental limitation and capability one is referred to as the max type construction resulting in a lipschitz continuous lyapunov function the other is the sum type construction resulting in a continuously differentiable lyapunov function this paper presents geometrical conditions under which the lyapunov construction is possible for a network comprising n 2 subsystems although the sum type construction for general n 2 has not yet been reduced to a readily computable condition we obtain a simple condition of iiss small gain in the case of n 2 it is demonstrated that the max type construction fails to offer a lyapunov function if the network contains subsystems which are not input to state stable iss

neutrino transport in core collapse supernovae abstract core collapse supernovae occupy a special place in the cosmic hierarchy for their role in disseminating and producing most elements in the universe heavier than hydrogen and helium without which life as we know it would not be possible these catastrophic events mark the end of a massive star s life and the birth of a neutron star or a black hole and are the most energetic explosions in the cosmos core collapse supernovae result when the iron core of a massive star becomes unstable at the end of the star s evolution collapses on itself rebounds at ultra high densities and produces a shock wave that will ultimately be responsible for disrupting the star as infalling core material passes through the shock it is compressed and heated and the core nuclei are dissociated broken up at the expense of thermal pressure producing energy behind the shock thereby weakening it in addition to this energy loss energy is carried away from the shocked region by massless particles know as neutrinos the shock stalls and is later thought to be revived by a neutrino heating mechanism at the time the shock stalls the core consists of an inner neutrinosphere radiating neutrinos and antineutrinos of three flavors electron muon and tau neutrinos and their antineutrinos this inner core will ultimately radiate away its thermal energy cool and go on to form a neutron star or a black hole revival of the stalled shock above the neutrinosphere is mediated by the absorption of electron neutrinos and antineutrinos emerging from the radiating proto neutron star this heating depends sensitively on the neutrino luminosities spectra and distribution of neutrino direction cosines in the region behind the shock in turn this depends on the neutrino transport through three regions the neutrino thick diffusion region deep within the core below the neutrinosphere the semitransparent region encompassing the neutrinosphere and the neutrino thin streaming region at larger radii sufficient accuracy for a definitive simulation of the supernova outcome can be obtained only via a solution of the neutrino boltzmann transport equations and their coupling to the hydrodynamics equations governing the evolution of the core material in this article we present a numerical method to solve the neutrino boltzmann equations coupled to the core hydrodynamics spherical symmetry is assumed but our methods extend to multidimensional boltzmann transport simulations with the assumption of spherical symmetry radius is the only spatial variable rendering the simulation at least as far as the spatial dimensions are concerned one dimensional however as we will discuss the boltzmann equation is a phase space equation in radius and neutrino direction cosine and energy and therefore inherently multidimensional even when spherical symmetry is assumed we also present the results of comparisons of multigroup flux limited diffusion approximate neutrino transport and boltzmann exact neutrino transport in post core bounce supernova environments with an eye toward the quantities central to the neutrino heating shock revival mechanism multigroup flux limited diffusion is the most sophisticated transport approximation implemented thus far in core collapse supernova simulations and will be described in some detail in this article our results demonstrate that differences significant to shock revival are obtained with the two transport schemes supporting the claim that accurate neutrino transport is paramount in simulations of these important cosmic events we discuss the ramifications our results have for our ongoing simulations of core collapse supernovae with exact boltzmann neutrino transport

non local stabilization of a spherical inverted pendulum we design a non linear stabilizing control law for a four degree of freedom spherical inverted pendulum the pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint the joint is free to move in the plane under the influence of a planar force the upright position is an unstable equilibrium of the uncontrolled system because of gravity the objective is to design a controller so that it stabilizes the upright position starting from any position in the upper hemisphere with arbitrary velocity we achieve this by first transforming the original system to an appropriate upper triangular form and then designing a controller which incorporates a high gain design with the method of non linear forwarding the control law is evaluated through computer simulations

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

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

saturated stabilization for an uncertain cascaded system subject to an oscillator abstract this paper investigates saturated stabilization of an uncertain cascaded system that consists of an uncertain double integrator and an uncertain oscillator the saturation reduction analysis is carried out by using the time interval based contradiction approach while the exponential stability analysis of the corresponding reduced system is conducted by using the hurwitz lemma in doing the saturation reduction analysis an intractable problem is how to estimate the states of the oscillator fully using the property of saturation functions as well as the technique of lyapunov inequalities we can first estimate the states of the oscillator and then achieve the time derivative bounds that some saturated terms possess in a finite time this has helped to carry out the saturation reduction analysis as the applications of the suggested algorithm the stabilizing controllers have been provided for two benchmark systems the uncertain two mass spring and the translational oscillator with a rotational actuator tora

robust stabilization via saturated feedback in this paper we deal with the problem of stabilization of uncertain systems in the presence of input constraint first algebraic conditions are derived for input to state stability of linear system with saturated linear feedback of low dimension then a recursive design procedure is derived for robust stabilization of block upper triangular nonlinear systems with feedforward structure

computational methods for nucleosynthesis and nuclear energy generation this review concentrates on the two principle methods used to evolve nuclear abundances within astrophysical simulations evolution via rate equations and via equilibria because in general the rate equations in nucleosynthetic applications form an extraordinarily stiff system implicit methods have proven mandatory leading to the need to solve moderately sized matrix equations efforts to improve the performance of such rate equation methods are focused on efficient solution of these matrix equations by making best use of the sparseness of these matrices recent work to produce hybrid schemes which use local equilibria to reduce the computational cost of the rate equations is also discussed such schemes offer significant improvements in the speed of reaction networks and are accurate under circumstances where calculations with complete equilibrium fail

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

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

brief paper a degree of flexibility in lyapunov inequalities for establishing input to state stability of interconnected systems in this paper a novel approach to constructing flexible lyapunov inequalities is developed for establishing input to state stability iss of interconnection of nonlinear time varying systems it aims at a useful tool for using nonlinear small gain conditions by allowing some flexibility in lyapunov inequalities each subsystem is to satisfy in the application of the iss small gain theorem achieving a lyapunov inequality conforming to a nonlinear small gain condition is not a straightforward task the proposed technique provides us with many lyapunov inequalities with which a single trade off condition between subsystems gains can establish the iss property of the interconnected system proofs are based on explicit construction of lyapunov functions

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 semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

output feedback stabilization and approximate and restricted tracking for a class of cascaded systems in this note we discuss the problems of output feedback stabilization for a class of cascaded systems and of approximate and restricted output regulation for general nonlinear systems it is shown that global output feedback stabilization for a class of systems in feedforward form can be achieved with a dynamic feedback law yielding bounded control and relying on the introduction of a reduced order observer the above result together with standard tools borrowed from the output regulator theory is instrumental to construct dynamic control laws achieving approximate disturbance rejection and output tracking in the presence of small disturbance reference signals generated by a known exosystem

analysis of input to state stability for discrete time nonlinear systems via dynamic programming the input to state stability iss property for systems with disturbances has received considerable attention over the past decade or so with many applications and characterizations reported in the literature the main purpose of this paper is to present analysis results for iss that utilize dynamic programming techniques to characterize minimal iss gains and transient bounds these characterizations naturally lead to computable necessary and sufficient conditions for iss our results make a connection between iss and optimization problems in nonlinear dissipative systems theory including l 2 gain analysis and nonlinear h theory as such the results presented address an obvious gap in the literature

on stability and stabilization of the linearized spacecraft attitude control system with bounded inputs lyapunov stability of the roll yaw and pitch subsystems of a linearized spacecraft attitude control system are re examined along the lines of a previously proposed jordan form based approach it is found that the roll yaw subsystem is lyapunov stable for inertially symmetric spacecraft with repeated eigenvalues on the imaginary axis which cannot be asserted by the existing characteristic equation based approach globally stabilizing controllers with bounded linear feedback are then designed for such spacecraft and the optimal feedback gain is designed such that the convergence rate of the linearized closed loop system is maximized the proposed method is also applicable to inertially symmetric spacecraft with magnetic actuators

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

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

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

a 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

discrete time lyapunov based small gain theorem for parameterized interconnected iss systems input to state stability iss of a feedback interconnection of two discrete time iss systems satisfying an appropriate small gain condition is investigated via the lyapunov method in particular an iss lyapunov function for the overall system is constructed from the iss lyapunov functions of the two subsystems we consider parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used in controller design for a sampled data system

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 regulation with nonlinear internal models this paper addresses the problem of semi global nonlinear output regulation for a class of nonlinear systems possessing a nonlinear internal model it is shown that under appropriate and verifiable hypotheses the standard assumption that the feed forward inputs needed to keep the zero error manifold invariant satisfy a linear differential equation can be weakened

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

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

trading the stability of finite zeros for global stabilization of nonlinear cascade systems analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system it is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term below this limit global stabilization is achieved by smooth static state feedback beyond this limit various examples illustrate that controllability of the cascade may be lost making it impossible to achieve large regions of attractions

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

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

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

positive p_n closures we introduce a modification to the standard spherical harmonic closure used with linear kinetic equations of particle transport while the standard closure is known to produce negative particle concentrations the modification corrects this defect by requiring that the ansatz used to close the equations itself be a nonnegative function we impose this requirement via explicit constraints in a quadratic optimization problem