w stability and local input output stability results a new type of input output stability is defined based on the use of a sobolev space w w is well suited like the lebesgue space l sub 2 to obtain stability characterizations in the time and frequency domains moreover if compared with l sub 2 w has additional properties which enable one to establish local stability results a local version of the small gain theorem is established in this framework as well as some consequences of this result in particular local versions of the passivity theorem and of the circle criterion the relationship between w stability and asymptotic stability is studied

gain scheduled and nonlinear systems dynamic analysis by velocity based linearization families a family of velocity based linearizations is proposed for a nonlinear system in contrast to the conventional series expansion linearization a member of the family of velocity based linearizations is valid in the vicinity of any operating point not just an equilibrium operating point the velocity based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated using velocity based linearizations stability conditions are derived for both smooth and non smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily perhaps excessively small neighbourhood about the equilibrium operating points inherent in existing frozen input theory for systems where there is no restriction on the rate of variation the velocity based linearization analysis is global in nature the analysis techniques developed although quite general are motivated by the gain scheduling design

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

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

j inner outer factorization j spectral factorization and robust control for nonlinear systems the problem of expressing a given nonlinear state space system as the cascade connection of a lossless system and a stable minimum phase system inner outer factorization is solved for the case of a stable system having state space equations affine in the inputs the solution is given in terms of the stabilizing solution of a certain hamilton jacobi equation the stable minimum phase factor is obtained as the solution of an associated nonlinear spectral factorization problem as an application one can arrive at the solution of the nonlinear h sub spl infin control problem for the disturbance feedforward case

a local form of small gain theorem and analysis of feedback volterra systems the requirement of evaluating a gain over the entire signal space is one of the restrictions in the traditional small gain theorem in this paper a local form of small gain theorem is presented it yields a bound on the external signal that guarantees that the magnitude of the specified signal along the closed loop stays within a certain region and hence it is useful in addressing the signal magnitude dependent stability problem the theorem is used to analyze the feedback properties of a volterra series system as well as an inverse or pseudo inverse volterra system improvement over existing results is demonstrated both theoretically and via numerical examples

nonlinear h infinity control and related problems of homogeneous systems in this paper the problems of h infinity control and related l2 gain of nonlinear homo geneous systems are considered first of all l2 gains of homogeneous stable systems are estimated with a method in light of hamilton jacobi inequalities secondly by virtue of hamilton jacobi isaacs hji inequality the nonlinear h infinity induced l2 gain problem of a class of systems with homogeneous vector fields is discussed and global control law is given under an assumption similar to the one of stabilizability of linear systems then following the previous results homogeneous systems with higher degree perturbed terms are studied finally the analysis of finite test of homogeneous systems with perturbed parameter is presented

characterization of the strict bounded real condition of nonlinear systems this paper is concerned with the strict bounded real condition of nonlinear systems which plays an important role in the nonlinear h sub spl infin control theory namely a necessary and sufficient condition for nonlinear systems to be internally asymptotically stable and to have the l sub 2 gain spl gamma is given via the hamilton jacobi equation with a stabilizing solution although some assumptions are required

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

model reference control system design for norm uncertain plants given a general non linear plant a method is presented for designing model reference feedback controllers for the plant it is shown that the feedback controllers produced will guarantee prespecified closed loop properties if the error between the plant and model lies within computable bounds in particular an upper bound on the tracking error is established and conditions are given that ensure closed loop stability

an input output based robust stabilization criterion for neural network control of nonlinear systems a stabilization method based on the input output conicity criterion is presented conventional learning algorithms are applied to adjust the controller dynamics and robust stability of the closed loop system is guaranteed by modifying the training patterns which yield unstable behavior the methodology developed expands the class of nonlinear systems to be controlled using neural control schemes so that the stabilization of a broad class of neural network based control systems even with unknown dynamics is assured straightforwardness in the application of this method is evident in contrast to the lyapunov function approach

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

multiple imputation under bayesianly smoothed pattern mixture models for non ignorable drop out conventional pattern mixture models can be highly sensitive to model misspecification in many longitudinal studies where the nature of the drop out and the form of the population model are unknown interval estimates from any single pattern mixture model may suffer from undercoverage because uncertainty about model misspecification is not taken into account in this article a new class of bayesian random coefficient pattern mixture models is developed to address potentially non ignorable drop out instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern mixture models we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical bayesian model that allows random variation across groups using real and simulated data we show that multiple imputation under a three level linear mixed effects model which accommodates a random level due to drop out groups can be an effective method to deal with non ignorable drop out by allowing model uncertainty to be incorporated into the imputation process

string stability of interconnected systems introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems intuitively string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded it is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input output stable the authors derive sufficient weak coupling conditions which guarantee the asymptotic string stability of a class of interconnected systems under the same weak coupling conditions string stable interconnected systems remain string stable in the presence of small structural singular perturbations in the presence of parameter mismatch these weak coupling conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient based parameter adaptation law is used and that the states of all the systems go to zero asymptotically

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

connections between local stability in lyapunov and input output senses the concept of gain over set was recently introduced as a tool for local input output analysis of nonlinear systems in this setting the finiteness of the gain over set defines a local stability in the input output sense in this paper we show that the finite gain over ball stability is related to the local stability in the sense of lyapunov

some statistical properties of a family of continuous univariate distributions abstract a new two parameter family of continuous univariate distributions on the interval 1 1 is introduced and some properties are given it is shown that parameters and v are globally orthogonal in the fisher information sense and that to some extent they have the properties of a location parameter and a precision parameter respectively a pivotal statistic is constructed whose distribution is independent of the location parameter finally the connection with ultraspherical functions and brownian motion is described

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

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

a generalization of the small gain theorem for nonlinear feedback systems abstract a generalization is given of the usual small gain theorem which allows greater flexibility in use of gain bounds for stability analysis of nonlinear feedback systems

robust stabilization of nonlinear systems by h state feedback abstract this paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback first a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty second based on the obtained robust stability condition a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some h state feedback control

qualitative equivalences of iss and lp gain stability properties for discrete time nonlinear systems input to state stability iss and inputoutput l2 gain are two important robust stability concepts in analyzing the interconnections of nonlinear dynamical systems in this paper we demonstrate several qualitative equivalences between different iss related properties and lp gain properties for discrete time systems via nonlinear changes of coordinates prior to that certain summation to summation estimates are shown to be equivalent to the standard definitions of iss and integral iss iiss which lead to sufficient lyapunov function conditions to verify lp gain properties combined with known results on the equivalence of 0 input global asymptotic stability and iiss and a superposition principle we subsequently outline interesting implicative relationships between various discrete time robust stability properties

asymptotic properties of incrementally stable systems it is shown that incremental stability of an input output operator ensures asymptotic stability of any equilibrium pair x sub e u sub e of its state representation if suitable minimality assumptions hold

design for h almost disturbance decoupling problem with internal stability via state or measurement feedback singular perturbation approach an almost disturbance decoupling technique guaranteeing internal stability of a linear system while using either state feedback or only measurement feedback is considered under a set of necessary and sufficient conditions a state feedback controller is explicitly constructed similarly a full or reduced order observer based measurement feedback controller is explicitly constructed under a set of necessary and sufficient conditions all the developed controllers guarantee the asymptotic stability of the closed loop system in the absence of disturbances furthermore they can reduce h norm of the transfer function from the external disturbance to the controlled output to any arbitrarily specified value unlike other methods which merely give the solvability conditions our method explictly constructs them also our controllers are parametrized in terms of tuning parameters by the tuning of which the disturbance reflected in the output can be attenuated to any desired degree of accuracy