one dimensional behavior of singular n dimensional solutions of semilinear heat equations we consider u x t a solution of u t u u p 1 u that blows up at time t where u n 0 t p 1 n 2 p 0 in particular if in addition p 3 then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow up set finally we prove that the mere hypothesis that the blow up set is continuous implies that it is c 1 1 2 for any 0

profile for the imaginary part of a blowup solution for a complex valued semilinear heat equation abstract in this paper we consider the following complex valued semilinear heat equation t u u u p u c in the whole space r n where p n p 2 we aim at constructing for this equation a complex solution u u 1 i u 2 which blows up in finite time t and only at one blowup point a with the following estimates for the final profile u x t p 1 2 x a 2 8 p ln x a 1 p 1 u 2 x t 2 p p 1 2 p 1 2 x a 2 8 p ln x a 1 p 1 1 ln x a as x a note that the imaginary part is non zero and that it blows up also at point a our method relies on two main arguments the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to get the conclusion up to our knowledge this is the first time where the blowup behavior of the imaginary part is derived in multi dimension

new stabilization criteria for linear time varying systems with state delay and norm bounded uncertainties this note deals with the stabilization problem of a class of un certain linear time varying systems with state delay simple stabilizability criteria are proposed in terms of the global controllability of the nominal system the feature of this note is that the stabilizability conditions and stabilizing controllers do not involve the solution of any riccati differential equation and hence they are easy to verify and design index terms controllability lyapunov function riccati equation sta bilization state delay uncertain systems

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems an application to river pollution control we employ the stability result of thowsen on a class of linear delay systems containing uncertain elements and subject to uncertain inputs to manage a simple one reach model of a river system with time delay and subject to uncertain but bounded input as well as parameter disturbances two important indices of water quality namely biochemical oxygen demand bod and dissolved oxygen do are used as state variables while controls in the form of effluent discharge rate of bod and in stream aeration rate of do are employed to steer the system to a calculable neighborhood of a desired steady state and then maintain it there

brief delay dependent robust h control of uncertain linear state delayed systems this paper examines the problems of robust stabilization and robust h control for linear systems with a constant time delay in the state and subject to parameter uncertainty systems with norm bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers we develop methods of robust stabilization and robust h control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities the proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays

new delay dependent approach to robust stability and stabilization for takagi sugeno fuzzy time delay systems in this paper we consider new generalized delay dependent stability conditions of takagi sugeno fuzzy time delay systems in the literature both delay independent stability conditions and delay dependent stability conditions for fuzzy time delay systems have already been obtained however those conditions are rather conservative and do not guarantee a wide stability region this is also true in case of the robust stability for uncertain fuzzy time delay systems here we choose a generalized lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it in order to obtain generalized delay dependent stability conditions in fact these techniques lead to generalized and less conservative stability conditions that guarantee a wide stability region our delay dependent stability conditions thus obtained are given in terms of linear matrix inequalities lmis we give three examples to illustrate our results comparison with other stability conditions in the literature shows our conditions are the most powerful ones to guarantee the widest stability region we also consider the robust stability of fuzzy time delay systems with uncertain parameters applying the same techniques obtained for the stability conditions we obtain delay dependent sufficient conditions for the robust stability of uncertain fuzzy systems moreover we give a design method of robustly stabilizing controllers for uncertain takagi sugeno fuzzy time delay systems

robust h observer design of linear time delay systems with parametric uncertainty abstract this paper deals with the problem of h observer design for a class of uncertain linear systems with delayed state and parameter uncertainties this problem aims at designing the linear state observers such that for all admissible parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint independently of the time delay the time delay is assumed to be unknown and the parameter uncertainties are allowed to be norm bounded and appear in all the matrices of the state space model an effective matrix inequality methodology is developed to solve the proposed problem we derive the conditions for the existence of the desired robust h observers and then characterize the analytical expression of these observers in terms of some free parameters a numerical example demonstrates the validity and applicability of the present approach

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

new robust stability conditions and design of robust stabilizing controllers for takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems and it thus leads to a conservative fuzzy controller design as well we first consider rather relaxed robust stability conditions of uncertain fuzzy systems to this end we introduce an auxiliary system to the original fuzzy time delay system to obtain generalized delay dependent stability conditions such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay dependent stability conditions conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in terms of linear matrix inequalities lmis then we compare our delay dependent stability conditions with other conditions in the literature and show that our conditions guarantee the stability of a wider class of systems than others next we consider the robust stabilization problem with memoryless and delayed state feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give three examples that illustrate our results

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

a linear matrix inequality approach for robust control of systems with delayed states abstract this paper addresses the robust stabilization problem for uncertain systems with delayed states the parameter uncertainties are unknown but norm bounded and the delay is time varying in this study a linear matrix inequality lmi approach for robust stability analysis for the nominal unforced system and a method for robust stabilization for a class of uncertain delay systems via linear memoryless state feedback control are presented the results depend on the size of the delay and are given in terms of linear matrix inequalities

blowup profile for a complex valued semilinear heat equation abstract this paper is concerned with finite blow up solutions of a one dimensional complex valued semilinear heat equation we classify blow up solutions and derive their blow up profiles under some assumptions in particular we discuss the possibility of a nonsimultaneous blow up

independent of delay stability criteria for uncertain linear state space models new stability robustness criteria are presented for linear state space models with multiple uncertain time delays and structured parameter uncertainty using the lyapunov equation approach the proposed stability criteria are independent of the size of time delays some previous quadratic stability criteria for linear uncertain systems without time delays are included as special cases examples are used to illustrate the less conservative results of the proposed methods compared with existing ones in the literature

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

design of performance robustness for uncertain linear systems with state and control delays the linear systems considered in this paper are subject to uncertain perturbations of norm bounded time varying parameters and multiple time delays in system state and control the time delays are uncertain independent of each other and allowed to be time varying the integral quadratic cost criterion is employed to measure system performance using solutions of lyapunov and riccati equations a linear state feedback control law is proposed to stabilize the perturbed system and to guarantee an upper bound of system performance which is applicable to arbitrary time delays

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

stabilizability of linear time varying and uncertain linear systems feedback stabilization of linear time varying and uncertain linear systems is considered it is proved that given a stabilizing dynamic linear state feedback controller one can always construct a stabilizing nondynamic linear state feedback controller a similar result is shown for uncertain linear systems a linear time varying system can be stabilized by dynamic output feedback if and only if it admits a coprime factorization

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

memoryless stabilization of uncertain dynamic delay systems riccati equation approach the authors present a procedure for obtaining the memoryless linear state feedback control of uncertain dynamic delay systems the uncertainties are time varying and within a given compact set this method is an extension of the riccati equation approach proposed by i r petersen and c v hollot 1986 the extension is straightforward also the uncertainties do not need to satisfy the matching conditions

quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays abstract this paper deals with the quadratic stability and linear state feedback and output feedback stabilization of switched delayed linear dynamic systems with in general a finite number of non commensurate constant internal point delays the results are obtained based on lyapunov s stability analysis via appropriate krasovsky lyapunov s functionals and the related stability study is performed to obtain both delay independent and delay dependent results it is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a in general non unique stabilizing switching law when the system is polytopic stable at some interior point of the polytope but with non necessarily stable parameterizations at the vertices defining the subsystems it is also proved that two subsystems individually parametrized in different polytopic type sets which are not quadratically stable might be stabilized by a in general non unique switching law provided that a convexity type condition is fulfilled at each existing pair of vertices one corresponding to each subsystem some extensions are provided for a typical class of neutral time delay systems

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

robust kalman filtering for discrete time markovian jump systems with parameter uncertainty in this paper we examine the problem of robust kalman filtering for a class of linear uncertain discrete time systems with markovian jump parameters the underlying system is subjected to norm bounded time varying uncertainties in the state and measurement equations first stochastic quadratic stability of the system is studied then a linear state estimator is constructed such that the estimation error covariance is guaranteed to lie within certain bound for all admissible uncertainties the solution is given in terms of two coupled algebraic riccati equations

h control of discrete time linear systems with time varying delays in state this paper deals with the h control problems for discrete time linear systems with time varying delays in state in this paper the h control law is assumed to be a memoryless state feedback and the size of time varying delays considered is upper bounded the solution of the h control problem for discrete time linear systems with time varying delays in state can be obtained by solving an h control problem for auxiliary discrete time linear systems with no time delays

blow up profile for the complex ginzburg landau equation abstract we construct a solution to the complex ginzburg landau equation which blows up in finite time t only at one blow up point we also give a sharp description of its blow up profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude two major difficulties arise in the proof the linearized operator around the profile is not self adjoint and it has a second neutral mode in the last section the interpretation of the parameters of the finite dimensional problem in terms of the blow up time and the blow up point gives the stability of the constructed solution with respect to perturbations in the initial data

robust stabilization of uncertain systems with time varying multistate delay the authors deal with the problem of stabilizing a class of uncertain linear systems with time varying multi state delay and subject to norm bounded parameter uncertainty via memoryless linear state feedback some sufficient conditions for the robust stabilizability are derived fur this class of uncertain systems if there exists a positive definite symmetric solution satisfying the algebraic riccati equation or inequality a suitable memoryless state feedback law can be derived also moreover all such parametric algebraic riccati inequalities have been transformed into some linear matrix inequality problems so there is no tuning of the parameters to gain a stabilizing solution

a blowup solution of a complex semi linear heat equation with an irrational power abstract in this paper we consider the following semi linear complex heat equation t u u u p u c in r n with an arbitrary power p p 1 we construct for this equation a complex solution u u 1 i u 2 which blows up in finite time t and only at one blowup point a moreover we also describe the asymptotics of the solution by the following final profiles u x t p 1 2 x a 2 8 p ln x a 1 p 1 u 2 x t 2 p p 1 2 p 1 2 x a 2 8 p ln x a 1 p 1 1 ln x a 0 as x a in addition to that since we also have u 1 0 t and u 2 0 t as t t the blowup in the imaginary part shows a new phenomenon unknown for the standard heat equation in the real case a non constant sign near the singularity with the existence of a vanishing surface for the imaginary part shrinking to the origin in our work we have succeeded to extend for any power p where the non linear term u p is not continuous if p is not integer in particular the solution which we have constructed has a positive real part we study our equation as a system of the real part and the imaginary part u 1 and u 2 our work relies on two main arguments the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to get the conclusion

robust control for parameter uncertain delay systems in state and control input in this note we present a robust control design method for parameter uncertain systems that have delay in both state and control input through a certain algebraic riccati inequality approach a state feedback controller is obtained the controller guarantees a stability for parameter uncertainties and delays

tecchnical communique robust stability and stabilization of linear delayed systems with structured uncertainty this paper shows criteria for robust stability and stabilization of linear state delayed systems with structured uncertainty we consider the structured uncertainty composed of repeated scalar block and full block forms and a time varying state delay delay dependent methods for robust stability and stabilization are provided in terms of linear matrix inequalities for linear systems with structured uncertainty and a time varying state delay the proposed methods give less conservative results than those obtained via the methods accounting for only norm boundedness of the uncertainty

global stabilizability of uncertain systems with time varying delays via dynamic observer based output feedback in this paper the dynamic observer based output feedback control for uncertain time delay systems with time varying delays is investigated a delay independent dynamic observer based output feedback control is proposed such that the feedback controlled system with time varying delays is globally asymptotically stable if some mild conditions are met an upper bound of arbitrary time varying delays without destroying stability is also given such that the asymptotic stability is preserved a numerical example is given to illustrate the use of our main results

robust stabilization for delayed discrete time fuzzy systems via basis dependent lyapunov krasovskii function abstract this paper deals with the robust control problem for a class of uncertain discrete time fuzzy systems with time delay the uncertainty is assumed to be of structured linear fractional form which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities by using basis dependent lyapunov krasovskii function a robust control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov krasovskii and the system matrices which make the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis the development represents an important step towards reducing the conservatism of previous design methods and the results also generalize earlier works for a more general parametric uncertainty structure numerical examples are also given to demonstrate the applicability of the proposed approach

blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term abstract we consider the following exponential reaction diffusion equation involving a nonlinear gradient term t u u u 2 e u x t r n 0 t 1 we construct for this equation a solution which blows up in finite time t 0 and satisfies some prescribed asymptotic behavior we also show that the constructed solution and its gradient blow up in finite time t simultaneously at the origin and find precisely a description of its final blowup profile it happens that the quadratic gradient term is critical in some sense resulting in the change of the final blowup profile in comparison with the case 0 the proof of the construction is inspired by the method of merle and zaag in 1997 it relies on the reduction of the problem to a finite dimensional one and uses the index theory to conclude one of the major difficulties arising in the proof is that outside the blowup region the spectrum of the linearized operator around the profile can never be made negative truly new ideas are needed to achieve the control of the outer part of the solution thanks to a geometrical interpretation of the parameters of the finite dimensional problem in terms of the blowup time and the blowup point we obtain the stability of the constructed solution with respect to perturbations in the initial data

optimal guaranteed cost control of uncertain discrete time delay systems this paper considers the problem of robust guaranteed cost control of linear discrete time delay systems with parametric uncertainties by matrix inequality approach the robust quadratic stability of the system is studied a control design method is developed such that the closed loop system with a cost function has a upper bound irrespective of all admissible parameter uncertainties and unknown time delays furthermore the upper bound cost can be optimized by incorporating with a minimization problem a numerical example is given to show the potential of the proposed techniques

robust control of state delayed systems with polytopic type uncertainties via parameter dependent lyapunov functionals abstract this paper considers the problem of robust stability and robust stabilization for linear systems with a constant time delay in the state and subject to real convex polytopic uncertainty first of all for robust stability problem we exploit new matrix inequalities characterization of delay dependent quadratic stability results demonstrate that it allows the use of parameter dependent lyapunov functionals and develop control design methods based on linear matrix inequalities lmis for solving the robust control problem next the problem of determining the maximum time delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by lmi techniques finally illustrative examples are given to demonstrate the advantage of these new representations

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

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

on the stability of uncertain systems with multiple time varying delays in this paper criteria for the global asymptotic stability of a class of uncertain systems with multiple time varying delays are proposed based on the improved razumikhin type theorem delay dependent and delay independent criteria are provided to guarantee the global asymptotic stability of such systems our main results are generalizations of some recent results reported in the literature in the case with multiple time varying delays a numerical example is also given to illustrate our results

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

on a conjecture of dao kurano abstract we prove a special case of a conjecture of dao kurano concerning the vanishing of hochster s theta pairing the proof uses adams operations on both topological k theory and perfect complexes with support

technical communique robust reliable control for a class of uncertain nonlinear state delayed systems this paper deals with the problem of robust reliable control design for a class of nonlinear uncertain state delayed systems the system under consideration involves state time delay parameter uncertainties and unknown nonlinear disturbances the nonlinearities are assumed to satisfy the boundedness condition and the parameter uncertainties are allowed to be time varying unstructured the purpose of this problem is to design the state feedback controller such that for all admissible uncertainties as well as actuator failures occuring among a prespecified subset of actuators the plant remains globally exponentially stable independently of the time delay an effective modified algebraic riccati equation approach is developed to solve the problem addressed it is shown that designed nonlinear time delay control systems provide guaranteed robust reliable stability despite possible actuator failures we present an illustrative example to demonstrate the applicability of the proposed design approach

construction of a blow up solution for the complex ginzburg landau equation in a critical case we construct a solution for the complex ginzburg landau equation in some critical case which blows up in finite time t only at one blow up point we also give a sharp description of its profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude the interpretation of the parameters of the finite dimension problem in terms of the blow up point and time allows to prove the stability of the constructed solution

robust stability and stabilization for uncertain takagi sugeno fuzzy time delay systems in this paper we consider robust stability and stabilization of uncertain takagi sugeno fuzzy time delay systems where uncertainties come into the state and input matrices some stability conditions and robust stability conditions for fuzzy time delay systems have already been obtained in the literature however those conditions are rather conservative and do not guarantee the stability and robust stability for a wide class of fuzzy systems this is true in case of designing stabilizing controllers for fuzzy time delay systems we first consider robust stability conditions of uncertain fuzzy systems conditions we obtain here are delay dependent conditions that depend on the upper bound of time delay and are given in linear matrix inequalities lmis an appropriate selection of lyapunov krasovskii function and introduction of free weighting matrices generalize robust stability conditions next we consider the stabilization problem with memoryless and delayed feedback controllers based on our generalized robust stability conditions we obtain delay dependent sufficient conditions for the closed loop system to be robustly stable and give a design method of robustly stabilizing controllers finally we give two examples that illustrate our results we compare our conditions with other stability conditions and show our conditions are rather generalized

uniform ultimate boundedness of the solutions of uncertain dynamic delay systems with state dependent and memoryless feedback control a continuous feedback controller is developed for a class of non linear time varying uncertain systems governed by functional differential equations with retarded arguments the form of the controller guarantees that under certain assumptions all solutions are uniformly bounded in norm for time t sufficiently largo in spite of the uncertainty in system parameters and input signals furthermore given any 0 the parameters in the description of the controller can be chosen such that the closed loop solutions all satisfy x t for large t

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

classification of singularities for blowing up solutions in higher dimensions consider the cauchy problem p u t u u p when x r n t 0 n 1 u x 0 u 0 x when x r n where p 1 and u 0 x is a continuous nonnegative and bounded function it is known that under fairly general assumptions on u 0 x the unique solution of p u x t blows up in a finite time by which we mean that lim sup sup u x t t t x r n in this paper we shall assume that u x t blows up at x 0 t t and derive the possible asymptotic behaviours of u x t as x t 0 t under general assumptions on the blow up rate

synthesis of controllers for continuous time delay systems with saturating controls via lmis the stabilization of linear continuous time systems with time delay in the state and subject to saturating controls is addressed sufficient conditions obtained via a linear matrix inequality lmi formulation are stated to guarantee both the local stabilization and the satisfaction of some performance requirements the method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed loop system is guaranteed when control saturations effectively occur

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

explicit solutions of the viscous model vorticity equation explicit solutions are found for the viscous version of the model vorticity equation recently proposed by p constantin p d lax and a majda where h w is the hilbert transform of w and v is a positive constant various properties of these solutions including the fact that they blow up after a finite time are discussed

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

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

solution of a nonlinear heat equation with arbitrarily given blow up points we consider the equation where i u is scalar valued and p 1 it has been proven that if u t blows up at time t the blow up points are finite in number and located in i our aim is to prove that this result is optimal that is for any given points x1 xk in i there is a solution u such that its blow up points are exactly x1 xk

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

hochster s theta invariant and the hodge riemann bilinear relations abstract let r be an isolated hypersurface singularity and let m and n be finitely generated r modules as r is a hypersurface the torsion modules of m against n are eventually periodic of period two i e tor i r m n tor i 2 r m n for i 0 since r has only an isolated singularity these torsion modules are of finite length for i 0 the theta invariant of the pair m n is defined by hochster to be length tor 2 i r m n length tor 2 i 1 r m n for i 0 h dao has conjectured that the theta invariant is zero for all pairs m n when r has even dimension and contains a field this paper proves this conjecture under the additional assumption that r is graded with its irrelevant maximal ideal giving the isolated singularity we also give a careful analysis of the theta pairing when the dimension of r is odd and relate it to a classical pairing on the smooth variety proj r

modulation theory for the blowup of vector valued nonlinear heat equations this paper is concerned with the blowup of solutions of the nonlinear vector valued heat equation ut u u p 1u u 0 u0 where u x t u1 x t um x t is a vector valued function from rn 0 t to rm and 1 p 3n 8 3n 4 working with the equation in similarity variables and using modulation theory and ideas from center manifold theory we obtain the asymptotic behavior of u in a backward space time parabola near any blowup point