linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

an m point boundary value problem of neumann type for a p laplacian like operator abstract let and be two odd increasing homeomorphism from r onto r with 0 0 0 0 and let f 0 1 r r r be a function satisfying caratheodory s conditions let a i r i 0 1 i 1 2 m 2 0 1 2 m 2 be given we are interested in the problem of existence of solutions for the m point boundary value problem x f t x x t 0 1 x 0 0 x 1 i 1 m 2 a i x i we note that this non linear m point boundary value problem is always at resonance since the associated m point boundary value problem x 0 t 0 1 x 0 0 x 1 i 1 m 2 a i x i has non trivial solutions x t r an arbitrary constant our results are obtained by a suitable homotopy leray schauder degree properties and a priori bounds

continuous discrete time observers for a class of mimo nonlinear systems this technical note addresses the observer design problem for a class of continuous time dynamical systems with non uniformly sampled measurements more specifically we propose an observer that runs in continuous time with an output error correction term that is updated in a mixed continuous discrete fashion the proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates nevertheless we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous time high gain observer coupled with an inter sample output predictor two design features of the proposed observer are worth emphasizing firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

a chain observer for nonlinear systems with multiple time varying measurement delays this paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time varying delays a modular approach is followed where subobservers are connected in cascade to achieve a desired exponential convergence rate chain observer when the delay is small a single step observer is sufficient to carry out the goal two or more subobservers are needed in the the presence of large delays the observer employs delay dependent time varying gains to achieve the desired exponential error decay the proposed approach allows to deal with vector output measurements where each output component can be affected by a different delay relationships among the error decay rate the bound on the measurement delays the observer gains and the lipschitz constants of the system are presented the method is illustrated on the synchronization problem of continuous time hyperchaotic systems with buffered measurements

brief paper on analytic and algebraic observability of nonlinear delay systems the observability of nonlinear delay systems has previously been defined in an algebraic setting by a rank condition on modules over noncommutative rings we introduce an analytic definition of observability to ensure the local uniqueness of state and initial conditions that correspond to a given input output behaviour it is shown that an algebraically observable delay system can be reformulated as a system of ordinary differential equations analytic observability is then decided by the local uniqueness of solutions to a boundary value problem for this ode system

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

multiplicity results for a three point boundary value problem at resonance this paper deals with second order three point boundary value problem u t f t u t t 0 1 u 0 0 u 1 u where f 0 1 r r is continuous 0 and 0 1 are given constants such that 1 we develop the methods of lower and upper solutions by the connectivity properties of the solution set of parameterized families of compact vector fields as applications of these methods we get several multiplicity results for the problems under consideration

state estimation for invariant systems on lie groups with delayed output measurements this paper proposes a state estimation methodology for invariant systems on lie groups where outputs of the system are measured with delay the proposed method is based on cascading an observer and a predictor the observer uses delayed measurements and provides estimates of delayed states the predictor uses those estimates together with the current inputs of the system to compensate for the delay and to provide a prediction of the current state of the system we consider three classes of left invariant right invariant and mixed invariant systems and propose predictors tailored to each class the key contribution of the paper is to exploit the underlying symmetries of systems to design novel predictors that are computationally simple and generic in the sense that they can be combined with any stable observer or filter we provide a rigorous stability analysis demonstrating that the prediction of the current state converges to the current system trajectory if the observer state converges to the delayed system trajectory the good performance of the proposed approach is demonstrated using a sophisticated software in the loop simulator indicating the robustness of the observer predictor methodology even when large measurement delays are present

truncated predictor feedback control for exponentially unstable linear systems with time varying input delay abstract the stabilization of exponentially unstable linear systems with time varying input delay is considered in this paper we extend the truncated predictor feedback tpf design method which was recently developed for systems with all poles on the closed left half plane to be applicable to exponentially unstable linear systems assuming that the time varying delay is known and bounded the design approach of a time varying state feedback controller is developed based on the solution of a parametric lyapunov equation an explicit condition is derived for which the stability of the closed loop system with the proposed controller is guaranteed it is shown that for the stability of the closed loop system the maximum allowable time delay in the input is inversely proportional to the sum of the unstable poles in the plant the effectiveness of the proposed method is demonstrated through numerical examples

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

observer design for nonlinear systems under unknown time varying delays the design of observers for nonlinear systems with unknown time varying bounded delays on both state and input still constitutes an open problem in this technical note we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a lyapunov krasovskii functional suitable choice sufficient conditions are provided to prove the practical stability of the observer it is shown that the observation error is bounded and depends on the size of two parameters the known upper bound delay of the unknown time varying function delay and the instantaneous state dynamic variation furthermore for the particular case of constant known time delay the convergence of the proposed observer becomes exponential the feasibility of the proposed strategy is illustrated by a numerical example

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

on the lower bound of net driving power in controlled duct flows we examine mathematically the lower bound of the net driving power i e the summation of pumping and actuation powers of a controlled duct flow under a constant flow rate the net power in a duct with arbitrary cross section in the presence of the inertial term blowing suction from the wall and arbitrary body forces can be decomposed into four terms 1 dissipation due to the velocity profile of the stokes flow in other words pumping power for the stokes flow 2 dissipation due to deviation of the mean velocity from the stokes flow profile 3 dissipation due to velocity fluctuations and 4 correlation between the wall pressure of the stokes flow and the time averaged blowing suction velocity of these the first three terms are shown to be non negative while the sign of the fourth term is indefinite the fourth term vanishes in cases where the duct has a constant shape cross section such as cylindrical pipes and plane channels namely in such cases the lower bound of net power is exactly given by the dissipation rate pumping power of the stokes flow at the same flow rate

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

spectral properties of p laplacian problems with neumann and mixed type multi point boundary conditions abstract we consider the boundary value problem consisting of the p laplacian equation 1 p u p u on 1 1 where p 1 p s s p 1 sgn s for s r r together with the multi point boundary conditions 2 p u 1 i 1 m i p u i or 3 u 1 i 1 m i u i or a mixed pair of these conditions with one condition holding at each of x 1 and x 1 in 2 3 m 1 are integers i 1 1 1 i m and the coefficients i satisfy i 1 m i 1 we term the conditions 2 and 3 respectively neumann type and dirichlet type boundary conditions since they reduce to the standard neumann and dirichlet boundary conditions when 0 given a suitable pair of boundary conditions a number is an eigenvalue of the corresponding boundary value problem if there exists a non trivial solution u an eigenfunction the spectrum of the problem is the set of eigenvalues in this paper we obtain various spectral properties of these eigenvalue problems we then use these properties to prove rabinowitz type global bifurcation theorems for related bifurcation problems and to obtain nonresonance conditions in terms of the eigenvalues for the solvability of related inhomogeneous problems

on output transformations for state linearization up to output injection steering a nonlinear system into a so called state affine one up to output injection by change of coordinates is of much interest for observer design this interest is preserved by also considering changes of output the purpose of the paper is then to provide computable conditions for existence of output transformations making a system which is not transformable into a state affine one up to output injection by only a change of coordinates to become so after a change of output such a characterization enlarges the class of systems for which an observer is available

joint state estimation and delay identification for nonlinear systems with delayed measurements the problem of state estimation for nonlinear systems with unknown state or measurement delays is still an open problem in this paper we consider the case of measurement delay and propose an approach that combines a delay identifier with a suitable high gain observer in order to achieve simultaneous estimation of state and delay we provide sufficient conditions that guarantee the exponential convergence to zero of the errors globally with respect to the system variables and locally with respect to the delay estimation we validate the method through an example concerning population models

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

some multipoint boundary value problems of neumann dirichlet type involving a multipoint p laplace like operator abstract let and be two increasing homeomorphisms from r onto r with 0 0 0 0 let f 0 1 r r r be a function satisfying caratheodory s conditions and for each i i 1 2 m 2 let a i r r be a continuous function with i 1 m 2 a i 0 1 i 0 1 0 1 2 m 2 1 in this paper we first prove a suitable continuation lemma of leray schauder type which we use to obtain several existence results for the m point boundary value problem u f t u u t 0 1 u 0 0 u 1 i 1 m 2 u i a i u i we note that this problem is at resonance in the sense that the associated m point boundary value problem u t 0 t 0 1 u 0 0 u 1 i 1 m 2 u i a i u i has the non trivial solution u t where r is an arbitrary constant vector in view of the assumption i 1 m 2 a i 0 1

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

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

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

delay dependent robust stability and stabilization of uncertain linear delay systems a linear matrix inequality approach this paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time delay the uncertainty is assumed to be norm bounded and appears in all the matrices of the state space model we develop methods for robust stability analysis and robust stabilization the proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities

sampled data chain observer design for a class of delayed nonlinear systems the problem of observer design is addressed for a class of triangular nonlinear systems with not necessarily small delay and sampled output measurements one more difficulty is that the system stat

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

an observer for a class of nonlinear systems with time varying observation delay abstract this paper presents a state observer for drift observable nonlinear systems when output measurements are affected by a known and bounded time varying delay the structure of the proposed observer is very simple and it is a generalization of an existing observer for undelayed systems the observer exhibits good performance in estimating the system state also in the presence of significant measurement delays the technique used to prove the asymptotical convergence to zero of the observation error based on the lyapunov razumikhin approach does not require any assumption about the dependence of the delay on the time

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

observation and stabilization of ltv systems with time varying measurement delay abstract this work deals with observer based output feedback stabilization of linear time varying ltv systems with time varying measurement delay the delay is modeled by a first order hyperbolic partial differential equation pde whose boundary condition evolves according to an ordinary differential equation ode namely the plant the overall system is thus represented by an ode pde cascade which is also the structure of the proposed observer the exponential stability of the estimation error is established for arbitrarily large time varying delays an observer based controller is also introduced and the closed loop stability is proved the separation principle holds and the design of both the observer and controller gains can be done as if there was no delay some simulations illustrate the feasibility of this approach

input output linearization of retarded non linear systems by using an extension of lie derivative this paper considers the input output linearization problem for retarded non linear systems which have time delays in the state by using an extension of the lie derivative for functional differential equations we derive a coordinates transformation and a static state feedback to obtain linear input output behaviour for a class of retarded non linear systems the obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones in addition we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback the effectiveness of the proposed technique is demonstrated through numerical simulations

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

ℋ observers design for a class of nonlinear time delay systems in descriptor form in this article we address the problem of designing an observer for a class of nonlinear time delay systems in descriptor form in both discrete time and continuous time cases we propose an observer design method using a particular lyapunov function that leads to solve a linear matrix inequality condition ensuring the convergence of the estimation error indeed we use a lyapunov function depending on the disturbances in order to avoid a specific obstacle in the stability analysis finally three numerical examples are provided in order to show the validity of the proposed method

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

controllability of driftless nonlinear time delay systems the controllability of a class of nonlinear driftless time delay systems is fully characterized for the first time this result is obtained within a newly introduced geometric approach moreover all those possible autonomous or non controllable elements which can depend on the delayed variables are also characterized when the system is not controllable and in consequence a canonical form of those systems is derived

a finite spectrum assignment for retarded non linear systems and its solvability condition this paper considers a finite spectrum assignment problem for retarded non linear systems first using extensions of the lie derivative and the lie bracket for differential difference equations we propose a finite spectrum assignment procedure for a class of retarded non linear systems then we derive a necessary and sufficient condition for the solvability of a class of finite spectrum assignment problems for retarded non linear systems the obtained condition is an extension of the condition for the exact linearization of finite dimensional non linear systems and the finite spectrum assignment of retarded linear systems with controllability over polynomial rings

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

optimal reset adaptive observer design abstract a reset adaptive observer reao is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined reset condition the inclusion of reset elements can improve the observer performance but it can also destroy the stability of the estimation process if the reao is not properly tuned as contribution a method to optimally tune the parameters and gains of the reao is presented they are optimally chosen by solving the l 2 gain minimization problem which can be rewritten as an equivalent lmi problem the effectiveness of the proposed method is checked by simulations comparing the results of an optimal reao with an optimal traditional adaptive observer

on existence of multiple positive solutions for ϕ laplacian multipoint boundary value abstract in this paper we consider the following multipoint boundary value problem with one dimensional laplacian x t q t f t x t x t 0 t 0 1 x 0 i 1 n 2 i x i x 1 i 1 n 2 i x i where is an odd and increasing homeomorphism i 0 1 with 0 1 2 n 2 1 i and i are nonnegative constants and f t x t x t is continuous and allowed to change sign by fixed point theorems we obtain new results on the existence of at least three positive solutions of this boundary value problem which includes and improves some related results in the relevant literature

a chain observer for nonlinear long constant delay systems this paper proposes a new state observer for nonlinear systems with non negligible and different time delays in the state output and input and lipschitz nonlinearity the proposed observer is composed of a chain of observers with similar algorithm each of them estimates the states in different time instants while the last observer estimates the state in the present time conditions for stability of the observer are translated into linear matrix inequalities lmis which facilitates the design of observer gains simulation results demonstrate effectiveness of this observer

observer based stabilisation of a class of nonlinear systems in the presence of measurement delay abstractin this paper the stabilising control problem for a class of nonlinear system in the presence of measurement delay is addressed a full order observer is designed to eliminate the effect of variable output time delay which is bounded and known then the estimated states are utilised for the state feedback control law to stabilise the considered control system lyapunov razumikhin approach is employed to analyse the stability of the closed loop system unlike the previous work the exponential convergence of the estimation error is ensured rather than asymptotic convergence by designing a delay dependent gain of the observer moreover comparison with similar work is also made in simulation to illustrate the effectiveness of the proposed strategy

observer with linear error dynamics for nonlinear multi output systems based upon nonlinear state coordinate transformations and a condensed dual brunovsk form for multi output systems a method for designing nonlinear state observers with linear error dynamics is presented necessary and sufficient conditions are provided for identifying the class of nonlinear systems for which state observers with linear error dynamics can be obtained

a dirichelet neumann m point bvp with a p laplacian like operator abstract let be odd increasing homeomorphisms from r onto r satisfying 0 0 0 and let f a b r r r be a function satisfying carath e odory s conditions let i r i a b i 1 m 2 a 1 2 m 2 b be given we are interested in the problem of existence of solutions for the m point boundary value problem u f t u u t a b u a 0 u b i 1 m 2 i u i in the resonance and non resonance cases we say that this problem is at resonance if the associated problem u 0 t a b u a 0 u b i 1 m 2 i u i has a non trivial solutions this is the case if and only if i 1 m 2 i 1 our results use topological degree methods interestingly enough in the non resonance case i e when i 1 m 2 i 1 the sign of degree for the relevant operator depends on whether i 1 m 2 i 1 or i 1 m 2 i 1

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

spectral properties of second order multi point p laplacian boundary value problems abstract we consider the multi point boundary value problem p u p u on 1 1 u 1 i 1 m i u i where p 1 p s s p 1 sgn s for s r r m 1 are integers i 1 1 1 i m and the coefficients i satisfy i 1 m i 1 a number r is said to be an eigenvalue of the above problem if there exists a non trivial solution u the spectrum is the set of eigenvalues in this paper we obtain some basic spectral and degree theoretic properties of this eigenvalue problem these results have numerous applications to more general problems as an example a rabinowitz type global bifurcation theorem is briefly described

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

gramian based uniform convergent observer for stable ltv systems with delayed measurements in this work an observer for a linear time varying system with delayed measurements is developed the delay is assumed to be unknown bounded and it can be time varying with no restriction on its rate of change the observer uses auxiliary signals related to the constructibility gramian of the system and it contains nonlin earities that provide a uniform fixed time convergence to a bounded region in the estimation error coordinates this means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time this property is new for the addressed class of systems the ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one and not directly on the delay size or its time derivative these properties are illustrated in a numerical simulation

a fundamental limit on the heat flux in the control of incompressible channel flow this paper proves that there are no zero net wall transpiration control strategies that can sustain net heat flux below the laminar level in an incompressible channel flow with constant temperature walls the result represents a fundamental limit on the performance of a controlled nonlinear system as measured by a linear cost function over a broad class of admissible initial conditions and control inputs not a zero sum tradeoff in the frequency domain or time domain both buoyancy effects via the boussinesq approximation and viscous heating effects are accounted for and phenomenological justification for the result is also given the boundedness of solutions of the two way coupled navier stokes energy equations when both buoyancy and viscous heating are accounted for is also discussed and a new proof of existence under an appropriate small data assumption is provided

boundary induced nonlinearities at small reynolds numbers we investigate the importance of boundary slip at finite reynolds numbers for mixed boundary conditions nonlinear effects are induced by the non homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction to explain the observed drag modification exact reciprocal relations in the presence of heterogeneous boundary conditions are derived the small reynolds number limit predicts a reduction of the mean flow rate from the creeping flow to be proportional to the second power of the reynolds number to further support our theoretical analysis numerical simulations with the lattice boltzmann method lbm and finite difference method fdm are performed and reveal a pronounced numerical efficiency of lbm with respect to fdm