non linear observer based on the euler discretization in this paper we present an estimator based on the euler discretization first we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated euler discretized system can be neglected otherwise we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time finally numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator

on stabilization of bilinear uncertain time delay stochastic systems with markovian jumping parameters in this paper we investigate the stochastic stabilization problem for a class of bilinear continuous time delay uncertain systems with markovian jumping parameters specifically the stochastic bilinear jump system under study involves unknown state time delay parameter uncertainties and unknown nonlinear deterministic disturbances the jumping parameters considered here form a continuous time discrete state homogeneous markov process the whole system may be regarded as a stochastic bilinear hybrid system that includes both time evolving and event driven mechanisms our attention is focused on the design of a robust state feedback controller such that for all admissible uncertainties as well as nonlinear disturbances the closed loop system is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are established to guarantee the existence of desired robust controllers which are given in terms of the solutions to a set of either linear matrix inequalities lmis or coupled quadratic matrix inequalities the developed theory is illustrated by numerical simulation

global bv solutions of compressible euler equations with spherical symmetry and damping abstract in this paper we study the global existence of bv solutions for compressible euler equations with spherical symmetry and damping using glimm s scheme the key point to consider is the combination of the geometric effects due to the spherical symmetry and the effects of the frictional damping on the total variation of the solutions by measuring the strength of the waves by r s where r s are the riemann invariants we construct a function which leads to the boundedness of the bv norm of the corresponding approximate solutions

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

global bv entropy solutions and uniqueness for hyperbolic systems of balance laws we consider the cauchy problem for n n strictly hyperbolic systems of nonresonant balance laws

observer design for autonomous discrete time nonlinear systems abstract we obtain a necessary and sufficient condition for a discrete time nonlinear system to be locally state equivalent to the nonlinear observer form the result looks similar to the continuous counterpart except for the fact that ad operation is utilized instead of ad operation

forward and backward shifts of vector fields towards the dual algebraic framework an algebraic framework for discrete time nonlinear control systems is introduced based on the forward and backward shifts of the vector fields it appears to be the dual of the framework based on the differential 1 forms as applications the characterization of accessibility and the solution to the static state feedback linearization problem are stated in terms of the given vector fields

linearization of discrete time nonlinear systems and a canonical structure linearizable nonlinear discrete time systems are described as a composition of diffeomorphisms linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms

sampled data adaptive control of a class of continuous nonlinear systems the problem is addressed of deriving sampled data control laws for a class of nonlinear continuous systems the concept of approximate state feedback linearizing control is defined for sampled data models arising from the sampling of continuous time systems such control laws are then designed for both non adaptive and adaptive cases and a detailed performance analysis is performed

isentropic gas flow for the compressible euler equation in a nozzle we study the motion of isentropic gas in a nozzle nozzles are used to increase the thrust of engines or to accelerate a flow from subsonic to supersonic nozzles are essential parts for jet engines rocket engines and supersonicwind tunnels in the present paper we consider unsteady flow which is governed by the compressible euler equation and prove the existence of global solutions for the cauchy problem for this problem the existence theorem has already been obtained for initial data away from the sonic state liu in commun math phys 68 141 172 1979 here we are interested in the transonic flow which is essential for engineering and physics although the transonic flow has recently been studied tsuge in j math kyoto univ 46 457 524 2006 lu in nonlinear anal real world appl 12 2802 2810 2011 these papers assume monotonicity of the cross section area here we consider the transonic flow in a nozzle with a general cross section area when we prove global existence the most difficult point is obtaining a bounded estimate for approximate solutions to overcome this we employ a new invariant region that depends on the space variable moreover we introduce a modified godunov scheme the corresponding approximate solutions consist of piecewise steady state solutions of an auxiliary equation which yield a desired bounded estimate in order to prove their convergence we use the compensated compactness framework

a functional integral approach to shock wave solutions of the euler equations with spherical symmetry ii abstract this is a continuation of 15 as is well known one dimensional conservation laws without source term have been extensively investigated after the foundamental paper of j glimm 3 and those with integrable source terms were solved by liu 6 7 etc for higher dimensional case with spherical symmetry makino 8 first proved a linear growth rate for solutions when p 2 where 1 but in order to get global existence for 1 and the decay property we need to find a uniform bound for the approximate solutions in 15 we introduced a new norm and a functional integral approach to prove a uniform bound for a model problem of euler equation in r 3 with spherical symmetry in order to overcome the geometric effects of spherical symmetry which leads to a non integrable source term we considered an infinite reflection problem and solved it by considering the cancellations between reflections of different orders in this paper we consider a system which describes the isentropic and spherically symmetric motion of gas flow surrounding a solid star with radius 1 and mass m it is interesting to note that the wave curves for this problem are no longer continuous and there is an extra term in the wave interaction estimates by introducing a new norm we prove a similar result as 15 in the appendix we present a local existence theorem for 1 which was also obtained by makino 9 by different method and we extend the results to the cases with different boundary conditions

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

convergence of shock capturing schemes for the compressible euler poisson equations we are concerned with approximate methods to construct global solutions with geometrical structure to the compressible euler poisson equations in several space variables a shock capturing numerical scheme is introduced to overcome the new difficulties from the nonlinear resonance of the system and the nonlocal behavior of the source terms the convergence and consistency of the shock capturing scheme for the equations is proved with the aid of the compensated compactness method then new existence results of the global solutions with geometrical structure are obtained the traces of the weak solutions are defined and then the weak solutions are proved to satisfy the boundary conditions the initial data are arbitrarily large withl bounds

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

nonlinear resonance for quasilinear hyperbolic equation the purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system for the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source analytical understanding is used to design a numerical scheme based on the random choice method an important physical example is transonic gas flow through a nozzle this analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow including such phenomena as nonlinear stability instability and changing types of waves

on the two dimensional gas expansion for compressible euler equations we investigate the problem of two dimensional unsteady expansion of an inviscid polytropic gas which can be interpreted as the collapse of a wedge shaped dam containing water initially with a uniform velocity we model this problem by isentropic euler equations the flow is quasi stationary and using hodograph transform we describe it by a partial differential equation of second order in the state space if it is irrotational initially furthermore this equation is reduced to a linearly degenerate system of three partial differential equations with inhomogeneous source terms these properties are used to prove that the flow is globally smooth when a wedge of gas expands into a vacuum and to analyze that shocks may appear in the interaction of four planar rarefaction waves

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

on dynamic input output linearization of discrete time nonlinear systems this paper studies the problem of linearizing the input output map of an analytic discrete time nonlinear system locally around a given trajectory necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state the proposed conditions are less restrictive than those obtained by lee and marcus for linearizing the input output map via a static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system firstly the solvability conditions are expressed in terms of the inversion algorithm secondly the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm

a functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

global solution of an initial value problem for two dimensional compressible euler equations abstract this paper is concerned with the existence of global continuous solutions of the expansion of a wedge of gas into a vacuum for compressible euler equations by hodograph transformation we first prove that the flow is governed by a partial differential equation of second order which is further reduced to a system of two nonhomogeneous linearly degenerate equations in the phase space under an irrotationality condition then this conclusion is applied to solving the problem that a wedge of gas expands into a vacuum which is actually a goursat type problem for these two equations in the supersonic domain

the immersion under feedback of a multidimensional discrete time non linear system into a linear system this paper deals with the problem of finding conditions which ensure the reproducibility of the input output behaviour of a linear analytic discrete time system by means of a linear discrete time system on this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved

axisymmetric solutions of the euler equations for polytropic gases we construct rigorously a three parameter family of self similar globally bounded and continuous weak solutions in two space dimensions for all positive time to the euler equations with axisymmetry for polytropic gases with a quadratic pressure density law we use the axisymmetry and self similarity assumptions to reduce the equations to a system of three ordinary differential equations from which we obtain detailed structures of solutions besides their existence these solutions exhibit familiar structures seen in hurricanes and tornadoes they all have finite local energy and vorticity with well defined initial and boundary values these solutions include the one parameter family of explicit solutions reported in a recent article of ours

existence of global solutions for unsteady isentropic gas flow in a laval nozzle in this paper we study the motion of isentropic gas in the laval nozzle the laval nozzle is the most important type of nozzle utilized in some turbines in particular we consider unsteady flows including transonic gas flows and prove the existence of global solutions for the cauchy problem in spite of its importance this problem has received little attention until now the most difficult point is to obtain bounded estimates for approximate solutions to overcome this we introduce a modified godunov scheme the corresponding approximate solutions consist of piecewise steady state solutions of an auxiliary equation and yield a sharper bounded estimate as a result we find an invariant region for our solutions finally in order to prove their convergence we use the compensated compactness framework

model simplification for switched hybrid systems abstract this paper is concerned with the problem of h model reduction for switched system which is an important class of hybrid systems frequently encountered in practical situations two sharply different approaches are proposed to solve this problem the first approach casts the model reduction into a convex optimization problem which is the first attempt to solve the model reduction problem by using linearization procedure the second one based on the cone complementarity linearization idea casts the model reduction problem into a sequential minimization problem subject to linear matrix inequality constraints both approaches have their own advantages and disadvantages concerning conservatism and computational complexity a numerical example illustrates the effectiveness of the proposed theories

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

stationary solutions to euler equations with spherical symmetry abstract in this paper as a first step to study the large time behavior of solutions to the compressible euler equations on a half line we consider the two classes of compressible euler equations and prove the existence of stationary solutions with spherical symmetry form the aim is to concentrate on understanding the influence of boundary conditions

sliding mode control of switched hybrid systems with stochastic perturbation this paper is concerned with the sliding mode control smc of a continuous time switched stochastic system a sufficient condition for the existence of reduced order sliding mode dynamics is derived and an explicit parametrization of the desired sliding surface is also given then a sliding mode controller is then synthesized for reaching motion moreover the observer based smc problem is also investigated some sufficient conditions are established for the existence and the solvability of the desired observer and the observer based sliding mode controller is synthesized finally numerical examples are provided to illustrate the effectiveness of the proposed theory

dimension reduction of compressible fluid models over product manifolds abstract in this paper we study the dimension reduction limits of the compressible navier stokes equations over product riemannian manifolds o m f such that dim m n and dim f d are arbitrary using the method of relative entropies we establish the convergence of the suitable weak solutions of the navier stokes equations on o to the classical solution of the limiting equations on m as 0 provided the latter exists in addition we also deduce the vanishing viscosity limit the limiting equations identified through our analysis contain the weight function a m r as a parameter where a x area of the fibre f x our work is based on and generalises the results in bella et al 2016 3 bella et al 2014 4 and maltese and novotn 2014 19 and it contains as special cases the physical models of circular nozzles thin plate limits and finite length longitudinal nozzles

compressible euler equations with general pressure law we study the hyperbolic system of euler equations for an isentropic compressible fluid governed by a general pressure law the existence and regularity of the entropy kernel that generates the family of weak entropies is established by solving a new euler poisson darboux equation which is highly singular when the density of the fluid vanishes new properties of cancellation of singularities in combinations of the entropy kernel and the associated entropy flux kernel are found

existence of global weak solutions to a special system of euler equation with a source ii general case abstract in this paper we apply the maximum principle and the theory of compensated compactness to establish an existence theorem for global weak solutions to the cauchy problem of the non strictly hyperbolic system a special system of euler equation with a general source term

on the compressible euler dynamics equations in transonic flow abstract this paper is concerned with the transonic flow in a variable area duct for the full compressible euler system we developed a generalized glimm method to confirm the existence of a solution for the initial boundary value problem the stability is resulted from the estimates on the interactions among the classical elementary waves and the perturbations caused by the operator splitting when the method is applied to the equations the limit of approximate solutions serves as a bv entropy solution in the cases where the duct has the positive material derivative or small l 1 norms of derivatives in particular both situations are consistent when the duct is expanded

on a weak solution for a transonic flow problem on essaie d etablir l existence de solutions faibles pour un ecoulement stationnaire bidimensionnel irrotationnel compressible non visqueux dans un canal de longueur infinie ou autour d un profil aerodynamique la vitesse de l ecoulement etant donnee a l infini

multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type we are concerned with the existence and stability of multidimensional transonic shocks for the euler equations for steady potential compressible fluids the euler equations consisting of the conservation law of mass and the bernoulli law for the velocity can be written as the following second order nonlinear equation of mixed elliptic hyperbolic type for the velocity potential r r 1 1 div d d 0 where the density function q is

axisymmetric solutions of the pressure gradient system a family of self similar and global bounded weak solutions are constructed rigorously for all positive time to the two dimensional pressure gradient system in this paper by using the axisymmetric and self similar assumptions the equations are reduced to a system of ordinary differential equations from which we obtain detailed structures of solutions as well as their existence on this basis we explore the behavior of characteristics near the sonic boundary

blowup phenomena of solutions to the euler equations for compressible fluid flow abstract the blowup phenomena of solutions is investigated for the euler equations of compressible fluid flow the approach is to construct special explicit solutions with spherical symmetry to study certain blowup behavior of multi dimensional solutions in particular the special solutions with velocity of the form c t x are constructed to show the expanding and blowup properties the solution with velocity of the form a t x a t for 1 and for any space dimensions is obtained as a corollary another conclusion is that there is only trivial solution with velocity of the form c t x 1 x for 1 and multi space dimensions

symmetric euler and navier stokes shocks in stationary barotropic flow on a bounded domain abstract we construct stationary solutions to the barotropic compressible euler and navier stokes equations in several space dimensions with spherical or cylindrical symmetry for given dirichlet data on a sphere or a cylinder we first construct smooth and radially symmetric solutions to the euler equations in the exterior domain on the other hand stationary smooth solutions in the interior domain necessarily become sonic and cannot be continued beyond a critical inner radius we then use these solutions to construct entropy satisfying shocks for the euler equations in the region between two concentric spheres or cylinders next we construct smooth navier stokes solutions converging to the previously constructed euler shocks in the small viscosity limit in the process we introduce a new technique for constructing smooth solutions which exhibit a fast transition in the interior to a class of two point boundary problems

vanishing viscosity solutions of the compressible euler equations with spherical symmetry and large initial data we are concerned with spherically symmetric solutions of the euler equations for multidimensional compressible fluids which are motivated by many important physical situations various evidences indicate that spherically symmetric solutions of the compressible euler equations may blow up near the origin at a certain time under some circumstance the central feature is the strengthening of waves as they move radially inward a longstanding open fundamental problem is whether concentration could be formed at the origin in this paper we develop a method of vanishing viscosity and related estimate techniques for viscosity approximate solutions and establish the convergence of the approximate solutions to a global finite energy entropy solution of the isentropic euler equations with spherical symmetry and large initial data this indicates that concentration is not formed in the vanishing viscosity limit even though the density may blow up at a certain time to achieve this we first construct global smooth solutions of appropriate initial boundary value problems for the euler equations with designed viscosity terms approximate pressure function and boundary conditions and then we establish the strong convergence of the viscosity approximate solutions to a finite energy entropy solution of the euler equations

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

existence of global smooth solution to the relativistic euler equations abstract in this paper we prove an existence theorem of global smooth solutions to the cauchy problem for the one dimensional relativistic euler equations the analysis is based on a priori estimates which are obtained by the characteristic method and maximum principle

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

some numerical aspects of approximate linearization of single input non linear systems we characterize approximate linearization to order m of a single input non linear system in terms of the existence of an integrating factor to order m 2 which is equivalent to the well known condition that a system of vector fields be order m 1 involutive we present a constructive method to obtain the required transformation for approximate linearization which results in substantial computational savings

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

global solutions to the compressible euler equations with geometrical structure we prove the existence of global solutions to the euler equations of compressible isentropic gas dynamics with geometrical structure including transonic nozzle flow and spherically symmetric flow due to the presence of the geometrical source terms the existence results themselves are new especially as they pertain to radial flow in an unbounded region vec x geqq 1 and to transonic nozzle flow arbitrary data withl bounds are allowed in these results a shock capturing numerical scheme is introduced to compute such flows and to construct approximate solutions the convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework

approximate and local linearizability of nonlinear discrete time systems we consider a single input non linear discrete time system of the form where x n u and f x u n 1 n is a c n valued function necessary and sufficient conditions for approximate linearizability are given for we also give necessary and sufficient conditions for local linearizability finally we present analogous results for multi input non linear discrete time systems

riemann problem with nonlinear resonance effects and well balanced godunov scheme for shallow fluid flow past an obstacle we are interested in characterizing the resonant behavior that occurs in a shallow water system with an arbitrary bottom topography the inhomogeneity introduced by the bottom topography elevation term in the system of equations is modeled by a linearly degenerate field strict hyperbolicity fails when one of the different nonlinear waves has a zero speed a proliferation of reflected waves can occur by interactions and then resonance effects are important for a transonic flow classical nonlinear waves interact with standing waves and exhibit overcompressive undercompressive and marginal compressive waves analytical understanding is used to introduce a new kind of numerical processing of the source term the riemann problem with nonlinear resonance is solved the so called well balanced godunov scheme is constructed which yields more accurate asymptotic states and preserves the balance between the source terms and flux terms the numerical flux and source terms are simultaneously solved in both space and time to overcome resonance

feedback linearization and lattice theory abstract the tools of lattice theory are applied to readdress the static state feedback linearization problem for discrete time nonlinear control systems unlike the earlier results that are based on differential geometry the new tools are also applicable for nonsmooth systems in case of analytic systems close connections are established between the new results and those based on differential one forms the mathematica functions have been developed that implement the algorithms methods from this paper

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory