feedback control for linear time invariant systems with state and control bounds in the presence of disturbances the problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered the only information required about the disturbances is a finite convex polyhedral bound discrete and continuous time systems are considered the property of positive d invariance of a region is introduced and it is proved that a solution of the problem is achieved by the selection of a polyhedral set s and the computation of a feedback matrix k such that s is positively d invariant for the closed loop system it is shown that if polyhedral sets are considered the solution involves simple linear programming algorithms however the procedure suggested requires a great amount of computational work offline if the state space dimension is large because the feedback matrix k is obtained as a solution of a large set of linear inequalities all of the vertices of s are required

two point b v p for multivalued equations with weakly regular r h s abstract a two point boundary value problem associated to a semilinear multivalued evolution equation is investigated in reflexive and separable banach spaces to this aim an original method is proposed based on the use of weak topologies and on a suitable continuation principle in frechet spaces lyapunov like functions are introduced for proving the required transversality condition the linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one some applications are given to the study of periodic and floquet boundary value problems of partial integro differential equations and inclusions appearing in dispersal population models comparisons are included with recent related achievements

systems of p laplacian differential inclusions with large diffusion abstract in this paper we consider coupled systems of p laplacian differential inclusions and we prove under suitable conditions that a homogenization process occurs when diffusion parameters become arbitrarily large in fact we obtain that the attractors are continuous at infinity on l 2 l 2 topology with respect to the diffusion coefficients and the limit set is the attractor of an ordinary differential problem

asymptotically autonomous multivalued cauchy problems with spatially variable exponents abstract we study the asymptotic behavior of a non autonomous multivalued cauchy problem of the form u t t div d t u t p x 2 u t u t p x 2 u t f t u t 0 on a bounded smooth domain in r n n 1 with a homogeneous neumann boundary condition where the exponent p c satisfies p min p x 2 we prove the existence of a pullback attractor and study the asymptotic upper semicontinuity of the elements of the pullback attractor a a t t r as t for the non autonomous evolution inclusion in a hilbert space h under the assumptions amongst others that f is a measurable multifunction and d l t is bounded above and below and is monotonically nonincreasing in time the global existence of solutions is obtained through results of papageorgiou and papalini

r matrices and generalized inverses four results are given that address the existence ambiguities and construction of a classical r matrix given a lax pair they enable the uniform construction of r matrices in terms of any generalized inverse of ad l for generic l a generalized inverse and indeed the moore penrose inverse is explicitly constructed the r matrices are in general momentum dependent and dynamical the construction applies equally to lax matrices with spectral parameter

a conjectured r matrix a new spectral parameter independent r matrix that depends on all of the dynamical variables is proposed for the elliptic calogero moser models the necessary and sufficient conditions for the existence this r matrix reduces to a determinantal equality involving elliptic functions the required identity appears new and is still unproven in full generality we present it as conjecture

abstract reaction diffusion systems with nonlocal initial conditions abstract we prove some sufficient conditions for the existence and global uniform asymptotic stability of c 0 solutions for a class of nonlinear delay reaction diffusion systems subjected to nonlocal initial conditions some applications to a specific reaction diffusion system are included

on a wildland fire model with radiation summary the 2 d simplied wildlandre model presented here is based on conservation laws and takes into account radiation as the dominant thermal transfer mechanism as well as convection which represents the eect of the wind and the slope the non dimensional equations are obtained using the frank kamenestkii change of variables the existence of weak solutions of the non linear reaction diusion problem obtained is established as a particular case of more general existence results using a compactness method the uniqueness of the weak solution is shown for a given initial data andxed parameters of the equations the approximate solution is obtained using a mixednite element method this preserves the continuity of theux through the inter element boundaries and allows to represent high gradients in the solution semi discrete error estimation is presented the convective term is solved by a splitting technique using godunov s method the numerical examples show the eciency of the algorithm in capturing there front even for critical values of the parameters copyright 2002 john wiley sons ltd

homogenization results for a coupled system of reaction diffusion equations abstract the macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction diffusion processes in periodic porous media is analyzed our mathematical model can be used for studying several metabolic processes taking place in living cells in which biochemical species can diffuse in the cytosol and react both in the cytosol and also on the organellar membranes the coupling of the concentrations of the biochemical species is realized via various properly scaled nonlinear reaction terms these nonlinearities which model at the microscopic scale various volume or surface reaction processes give rise in the macroscopic model to different effects such as the appearance of additional source or sink terms or of a non standard diffusion matrix

periodic solutions for a class of differential inclusions in general banach spaces abstract let x be a real banach space a d a x x an m accretive operator and f r d a x a multi function which is 2 periodic with respect to its first argument has nonempty closed convex and weakly compact values and is strongly weakly upper semicontinuous in this paper we prove the existence of at least one solution for the problem u t a u t f t f t f t u t u t u t 2 in the case in which f satisfies an appropriate sign condition

existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions in this paper we provide a sufficient condition for the existence of c0 solutions for a class of nonlinear functional differential evolution equation of the form u t au t f t t r f t f t u t ut t r u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r x c 0 d a x is a nonempty convex and weakly compact valued multi function and g cb d a c 0 d a

nonlocal impulsive fractional differential inclusions with fractional sectorial operators on banach spaces this paper investigates existence of pc mild solutions of impulsive fractional differential inclusions with nonlocal conditions when the linear part is a fractional sectorial operators like in bajlekova 2001 1 on banach spaces we derive two existence results of pc mild solutions when the values of the semilinear term f is convex as well as another existence result when its values are nonconvex further the compactness of the set of solutions is characterized

a class of nonlinear evolution equations subjected to nonlocal initial conditions abstract we prove the existence of c 0 solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions of the form u t a u t f t f t f t u t u 0 g u where a d a x x is an m accretive operator acting on the infinite dimensional banach space x f 0 2 d a x is an almost strongly weakly u s c multi function which satisfies an appropriate sign condition while g c 0 2 d a d a is a continuous function

on infinity norms as lyapunov functions for linear systems the note presents a construction of the lyapunov function defined by l sub spl infin sup n vector norm for both continuous and discrete time linear systems in contrast to the previous results no restrictions on the positions or multiplicity of system matrix eigenvalues are required

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

constrained regulation of linear systems abstract in this paper the linear constrained regulation problem without an assigned set of initial states is investigated this problem consists of the determination of a linear state feedback control law and of a set of admissible initial states d so that every trajectory of the resulting closed loop system which emanates from the set converges asymptotically to the origin without violation of the control constraints by applying well known results on the positive invariance of polyhedral sets an eigenstructure assignment approach to this problem is established if the number of unstable open loop eigenvalues does not exceed the number of control variables then this approach enables one to derive a linear state feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant this positively invariant set is the maximal admissible set of initial states for the control law under consideration for the case where the number of control variables is greater than the number of the unstable open loop eigenvalues a modified algorithm is proposed

set valued observers and optimal disturbance rejection a set valued observer also called guaranteed state estimator produces a set of possible states based on output measurements and models of exogenous signals we consider the guaranteed state estimation problem for linear time varying systems with a priori magnitude bounds on exogenous signals we provide an algorithm to propagate the set of possible states based on output measurements and show that the centers of these sets provide optimal estimates in an l sup spl infin induced norm sense we then consider the utility of set valued observers for disturbance rejection with output feedback and derive the following general separation structure an optimal controller can consist of a set valued observer followed by a static nonlinear function on the observed set of possible states a general construction of this function is provided in the scalar control case furthermore in the special case of full control i e the number of control inputs equals the number of states optimal output feedback controllers can take the form of an optimal estimate of the full state feedback controller

nonlocal diffusion second order partial differential equations abstract the paper deals with a second order integro partial differential equation in r n with a nonlocal degenerate diffusion term nonlocal conditions such as the cauchy multipoint and the weighted mean value problem are investigated the existence of periodic solutions is also studied the dynamic is transformed into an abstract setting and the results come from an approximation solvability method it combines a schauder degree argument with an hartman type inequality and it involves a scorza dragoni type result the compact embedding of a suitable sobolev space in the corresponding lebesgue space is the unique amount of compactness which is needed in this discussion the solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces

existence and asymptotic stability of periodic solution for evolution equations with delays abstract in this paper we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a hilbert space h u t a u t f t u t u t 1 u t n t r where a d a h h is a positive definite selfadjoint operator f r h n 1 h is a nonlinear mapping which is periodic in t and 1 2 n are positive constants we present essential conditions on the nonlinearity f to guarantee that the equation has periodic solutions or an asymptotically stable periodic solution the discussion is based on analytic semigroups theory and an integral inequality with delays

non crystallographic reduction of generalized calogero moser models we apply a recently introduced reduction procedure based on the embedding of non crystallographic coxeter groups into crystallographic ones to calogero moser systems for rational potentials the familiar generalized calogero hamiltonian is recovered for the hamiltonians of trigonometric hyperbolic and elliptic types we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio we explicitly show for the simplest of these non crystallographic models how the corresponding classical equations of motion can be derived from a lie algebraic lax pair based on the larger crystallographic coxeter group

topological theory of non autonomous parabolic evolution inclusions on a noncompact interval and applications in this paper we consider the topological structure of the solution set of non autonomous parabolic evolution inclusions with time delay defined on non compact intervals the result restricted to compact intervals is then extended to non autonomous parabolic control problems with time delay moreover as the applications of the information about the structure we establish the existence result of global integral solutions for non autonomous cauchy problems subject to nonlocal condition and prove the invariance of a reachability set for non autonomous control problems under single valued nonlinear perturbations finally some illustrating examples are supplied

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

nonlinear evolution inclusions topological characterizations of solution sets and applications this paper deals with a nonlinear delay differential inclusion of evolution type involving m dissipative operator and source term of multi valued type in a banach space under rather mild conditions the r structure of c0 solution set is studied on compact intervals which is then used to obtain the r property on non compact intervals secondly the result about the structure is furthermore employed to show the existence of c0 solutions for the inclusion mentioned above subject to nonlocal condition defined on right half line no nonexpansive condition on nonlocal function is needed as samples of applications we consider a partial differential inclusion with time delay and then with nonlocal condition at the end of the paper

on p laplacian differential inclusions global existence compactness properties and asymptotic behavior abstract in this work we consider coupled systems of p laplacian differential inclusions we obtain the global existence of solutions and good compactness properties in such way that the set of all possible solutions compose a generalized semiflow which has a global attractor for each pair of positive diffusion coefficients we also prove that the attractors are upper semicontinuous on positive finite diffusion parameters

periodic solutions of nonlinear evolution inclusions abstract in this paper we establish the existence of periodic trajectories for a class of nonlinear time varying evolution inclusions in which the multivalued term is nonconvex valued an example of a parabolic system is also presented in detail

compactness results with applications for nonautonomous coupled inclusions abstract in this work we provide compactness results which are generalizations of baras theorem for the case when the main operator is time dependent and we give applications for nonautonomous coupled inclusions proving that these multivalued problems define exact generalized processes

set valued observer design for a class of uncertain linear systems with persistent disturbance and measurement noise in this paper a class of linear systems affected by parameter variations additive noise and persistent disturbances is considered the problem of designing a set valued state observer which estimates a region containing the real state for each time instant is investigated the techniques for designing the observer are based on positive invariant set theory by constructing a set induced lyapunov function it is shown that the estimation error converges exponentially to a given compact set with an assigned rate of convergence

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

topological degree methods for perturbations of operators generating compact c 0 semigroups abstract the main aim of this paper is to construct a topological degree for maps a f m d a e where a densely defined closed operator a d a e of a banach space e is such that a is the generator of a compact c 0 semigroup and f m e is a locally lipschitz map defined on a neighborhood retract m e if m is a closed convex cone then a degree formula allowing an effective computation of the degree is proved this formula provides an infinite dimensional counterpart of the well known krasnosel skii theorem by the use of the introduced topological degree and an abstract result concerning branching of fixed points the bifurcation of periodic points of the parameterized boundary value problem u au f t u 0 u t m u 0 u t is studied examples of applications to partial differential equations are discussed

a viability result for a class of fully nonlinear reaction diffusion systems abstract we consider a class of abstract evolution systems governed by continuous perturbations of m dissipative operators and we prove a necessary and sufficient condition for a given locally closed set to be c 0 viable we conclude with a comparison result for a fully nonlinear reaction diffusion system

parameter dependent lyapunov functions and the popov criterion in robust analysis and synthesis many practical applications of robust feedback control involve constant real parameter uncertainty whereas small gain or norm bounding techniques guarantee robust stability against complex frequency dependent uncertainty thus entailing undue conservatism since conventional lyapunov bounding techniques guarantee stability with respect to time varying perturbations they possess a similar drawback in this paper we develop a framework for parameter dependent lyapunov functions a less conservative refinement of fixed lyapunov functions an immediate application of this framework is a reinterpretation of the classical popov criterion as a parameter dependent lyapunov function this result is then used for robust controller synthesis with full order and reduced order controllers

on abstract differential equations with state dependent non local conditions abstract in this paper we introduce the concept of state dependent nonlocal condition and study the existence and uniqueness of solution for a general class of abstract differential equations with state dependent delay subject to this class of conditions in this type of problem the nonlocal condition can be dependent on times or time intervals determined by the unknown solution some examples on partial differential equations with state dependent delay arising in population dynamics are presented

properties of the relaxed trajectories of evolution equations and optimal control this paper considers a class of nonconvex control problems in a banach space governed by a semilinear evolution equation and establishes the existence of admissible pairs then the introduction of measure valued controls convexifies the system and under general assumptions it is shown that the set of trajectories of the original system is dense in an appropriate topology in the set of relaxed trajectories some useful topological properties of the set of relaxed trajectories are also determined furthermore some optimization problems are solved and in many cases the values of the original and relaxed problems are shown to be equal finally another relaxation result is proved for a different class of systems described by a general nonlinear evolution equation

some new results for multi valued fractional evolution equations given a closed linear operator a in a banach space x and a multi valued function with convex closed values f 0 b c 0 x 2 x we consider the cauchy problem c d t u t au t f t u t t 0 b u t t t 0 where 0 c d t 0 1 represents the regularized caputo fractional derivative of order we concentrate on the case when the semigroup generated by a is noncompact and obtain nonemptyness of the solution set if in particular x is reflexive and f is weakly upper semicontinuous with respect to the second variable furthermore in this situation topological properties of the set of all solutions are considered

non autonomous evolution inclusions with nonlocal history conditions global integral solutions abstract this paper is concerned with nonlinear nonlocal differential inclusion of evolution type in frechet spaces defined on right half line the underlying feature of the inclusion under consideration is that it is non autonomous we obtain some compactness characterizations of integral solution sets for the inclusion without nonlinear perturbations then making use of these characterizations we derive a new existence result of global integral solutions for the original inclusion no invariance condition on the nonlinearity is involved the results we obtained here extend the semilinear case of the previous related ones such as i i vrabie existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions j funct anal 262 2012 1363 1391 and are new even for the case of the nonlinearity being a single valued function

separation of variables for the ruijsenaars system we construct a separation of variables for the classical n particle ruijsenaars system the relativistic analog of the elliptic calogero moser system the separated coordinates appear as the poles of the properly normalised eigenvector baker akhiezer function of the corresponding lax matrix two different normalisations of the ba functions are analysed the canonicity of the separated variables is verified with the use of the r matrix technique the explicit expressions for the generating function of the separating canonical transform are given in the simplest cases n 2 and n 3 taking the nonrelativistic limit we also construct a separation of variables for the elliptic calogero moser system

existence of solutions for a class of abstract differential equations with nonlocal conditions abstract we discuss the existence of mild classical and strict solutions for a class of abstract differential equations with nonlocal conditions our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution some concrete applications to partial differential equations are considered

existence for nonlinear evolution inclusions with nonlocal retarded initial conditions abstract in this paper we prove a sufficient condition for the global existence of bounded c 0 solutions for a class of nonlinear functional differential evolution equation of the form u t a u t f t t 0 f t f t u t u t 1 u t n t 0 u t g u t t 0 where x is a real banach space a is the infinitesimal generator of a nonlinear compact semigroup f r d a n 1 x is a nonempty convex weakly compact valued and almost strongly weakly u s c multi function and g c b d a c 0 d a is nonexpansive

existence for reaction diffusion systems a compactness method approach the authors study the existence of weak solutions for the following system ut u f u v vt v g u v in 0 t u v 0 on 0 t u 0 x u0 x v 0 x v0 x in the region rn with smooth boundary the functions r r are assumed to be continuous and nondecreasing with 0 0 0 u0 v0 l f g r2 2r with f an upper semicontinuous mapping u s c the following local existence results are shown 1 for the diffusive case i e when both and are strictly increasing with u s c g 2 for the semi diffusive case only one function is strictly increasing with g being either with separated variables i e having the form of the product or of the sum of two functions g u and h v or globally lipschitz with respect to its second variable i e g u v g u v l v v for each u b r v v r and some l l b additional conditions of linear form on the growth of f and g are indicated to guarantee global existence results

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

periodic solutions for nonlinear differential inclusions with multivalued perturbations abstract in this paper the periodic solutions for nonlinear differential inclusion governed by convex subdifferential and different perturbations are studied it is firstly proved that the differential inclusion has unique periodic solution if the perturbation function is a single valued function then by schauder s fixed point theorem and kakutani s fixed point theorem we prove that the differential inclusion has at least a periodic solution when the perturbation function is an upper semicontinuous or lower semicontinuous multifunction moreover the existence of the extremal solution for the differential inclusion is also studied finally based on one sided lipschitz osl assumption we prove the related relaxation theorem

existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions abstract this paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in banach spaces first using the approach of geometry of banach space hausdorff metric the measure of noncompactness and fixed point existence results are obtained we have removed from previous papers the crucial restriction on the semigroup then we establish the asymptotic properties of integral solutions when t finally for illustration a partial differential equation is worked out

well posed p laplacian problems with large diffusion abstract in this work we study the asymptotic behavior of p laplacian parabolic problems of the form u t d p u u p 2 u b u in a bounded smooth domain in r n and under neumann boundary conditions when the diffusion coefficient d becomes large we prove under suitable assumptions that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity