conewise linear systems non zenoness and observability conewise linear systems are dynamical systems in which the state space is partitioned into a finite number of nonoverlapping polyhedral cones on each of which the dynamics of the system is described by a linear differential equation this class of dynamical systems represents a large number of piecewise linear systems most notably linear complementarity systems with the p property and their generalizations to affine variational systems which have many applications in engineering systems and dynamic optimization the challenges of dealing with this type of hybrid system are due to two major characteristics mode switchings are triggered by state evolution and states are constrained in each mode in this paper we first establish the absence of zeno states in such a system based on this fundamental result we then investigate and relate several state observability notions short time and t time or finite time local global observability for the short time observability notions constructive finitely verifiable algebraic both sufficient and necessary conditions are derived due to their long time mode transitional behavior which is very difficult to predict only partial results are obtained for the t time observable states nevertheless we completely resolve the t time local observability for the bimodal conewise linear system for finite t and provide numerical examples to illustrate the difficulty associated with the long time observability

a new recursive identification algorithm for singularity free adaptive control reportedly guaranteeing the controllability of the estimated system is a crucial problem in adaptive control in this paper we introduce a least squares based identification algorithm for stochastic siso systems which secures the uniform controllability of the estimated system and presents closed loop identification properties similar to those of the least squares algorithm the proposed algorithm is recursive and therefore easily implementable its use however is confined to cases in which the parameter uncertainly is highly structured

positive soliton solutions for generalized quasilinear schrodinger equations with critical growth this paper is concerned with the positive solutions for generalized quasilinear schrodinger equations in rn with critical growth which have appeared from plasma physics as well as high power ultrashort laser in matter by using a change of variables and variational argument we obtain the existence of positive solutions for the given problem

on generalized bisection of n simplices a generalized procedure of bisection of n simplices is introduced where the bisection point can be an almost arbitrary point at one of the longest edges it is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton and an exact bound of the convergence speed in terms of diameter reduction is given for regular simplices which mark the worst case the edge lengths of each worst and best simplex generated by successive bisection are given up to depth n for n 2 and 3 the sequence of worst case diameters is provided until it is halved

quasilinear asymptotically periodic schrodinger equations with subcritical growth abstract in this article the existence of one solution for a class of asymptotically periodic equations in the euclidean space is established the basic tools employed here are the mountain pass theorem and the concentration compactness principle by using a change of variable the quasilinear equation is reduced to a semilinear equation whose respective associated functional is well defined in h 1 r n and satisfies the geometric hypotheses of the mountain pass theorem

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

existence multiplicity and concentration of solutions for generalized quasilinear schrodinger equations with critical growth in this paper we study the following generalized quasilinear schrodinger equations div e2g2 u u e2g u g u u 2 v x u f u g u g u 2 2g u x n where e 0 n 3 g is a c1 even function g 0 1 and g s 0 for all s 0 where g u 0ug t dt under some suitable conditions we study the existence multiplicity and concentration of solutions by the variational methods

algorithmic copositivity detection by simplicial partition we present new criteria for copositivity of a matrix i e conditions which ensure that the quadratic form induced by the matrix is nonnegative over the nonnegative orthant these criteria arise from the representation of the quadratic form in barycentric coordinates with respect to the standard simplex and simplicial partitions thereof we show that as the partition gets finer and finer the conditions eventually capture all strictly copositive matrices we propose an algorithmic implementation which considers several numerical aspects as an application we present results on the maximum clique problem we also briefly discuss extensions of our approach to copositivity with respect to arbitrary polyhedral cones

multiple model adaptive mixing control the discrete time case most of the work in multiple model adaptive control with various forms of switching focused on continuous time systems the purpose of this technical note is to extend the results of one approach the adaptive mixing control amc to discrete time systems further the technical note solves the tracking problem which has not been addressed in most schemes of this class stability and robustness properties of the amc scheme for discrete time systems are analyzed it is shown that in the ideal case when no disturbances or unmodeled dynamics are present the tracking error converges to zero in the non ideal case the mean square tracking error is of the order of magnitude of the modeling error provided the unmodeled dynamics satisfy a norm bound condition while these robustness results are conceptually similar to those of traditional robust adaptive control the proposed scheme does not suffer from the drawback of stabilizability of the estimated plant and in addition performs much better in simulation studies furthermore it allows well developed results from robust control to be incorporated in the design

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

ground state solutions for quasilinear schrodinger systems this paper is concerned with the quasilinear schrodinger systems in rn u a x 1 u 12 u 2 u 2 u 2 v u v b x 1 v 12 v 2 v 2 u v 2v u x 0 v x 0as x where 0 is a parameter 2 2 2 2 and 2 2nn 2 for n 3 2 for n 1 2 is the critical sobolev exponent by using the nehari manifold method and concentration compactness principle in the orlicz space we prove the existence of ground state solution which localize near the potential well int a 1 0 intb 1 0 for large enough

multiple positive solutions for linearly coupled nonlinear elliptic systems with critical exponent abstract this paper deals with the following system linearly coupled by nonlinear elliptic equations u 1 u u 2 2 u v x v 2 v v 2 2 v u x u v 0 on here is a smooth bounded domain in r n n 3 1 2 1 are constants 1 is the first eigenvalue of h 0 1 2 2 n n 2 is the sobolev critical exponent and r is a coupling parameter by variational method we prove that this system has a positive ground state solution for some 0 via a perturbation argument we show that this system also admits a positive higher energy solution when is small moreover the asymptotic behaviors of the positive ground state and higher energy solutions as 0 are analyzed

ground states for a class of critical quasilinear coupled superlinear elliptic systems abstract in this work we consider the following class of quasilinear coupled systems u a x u u 2 u g u x u 2 u v x r n v b x v v 2 v h v x v 2 v u x r n where n 3 and a b r n r are positive potentials r n r is a nonnegative continuous function 0 and 2 satisfying 2 2 on the nonlinear terms we assume that g h are in c 1 class which are superlinear functions at infinity and at the origin we deal with nonlinearities g and h being subcritical or critical the coupling term is a subcritical function which is superlinear at infinity our main theorem is stated without the well known ambrosetti rabinowitz condition at infinity using a change of variable we turn the quasilinear coupled system into a nonlinear coupled system where we establish a variational approach based on nehari method

piecewise lyapunov functions for robust stability of linear time varying systems in this paper we investigate the use of two term piecewise quadratic lyapunov functions for robust stability of linear time varying systems by using the so called s procedure and a special variable reduction method we provide numerically efficient conditions for the robust asymptotic stability of the linear time varying systems involving the convex combinations of two matrices an example is included to demonstrate the usefulness of our results

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

existence of ground state solutions for a quasilinear schrodinger equation with critical growth we establish the existence of ground state solutions for a quasilinear schrodinger equation u v x u u 2 u u 2 2 2 u u p 1 u in r n where n 3 2 2 n n 2 1 p 2 2 1 and 0 is a parameter we do not need the subcritical exponent p 3 which was used by several authors to conclude the existence of solution for the equation above

cone copositive piecewise quadratic lyapunov functions for conewise linear systems in this technical note cone copositive piecewise quadratic lyapunov functions pwq lfs for the stability analysis of conewise linear systems are proposed the existence of a pwq lf is formulated as the feasibility of a cone copositive programming problem which is represented in terms of linear matrix inequalities a constructive procedure for its solution is provided examples show the effectiveness of the approach also in the case of uncertain conewise linear systems

asymptotic stability of piecewise affine systems with filippov solutions via discontinuous piecewise lyapunov functions asymptotic stability of continuous time piecewise affine systems defined over a polyhedral partition of the state space with possible discontinuous vector field on the boundaries is considered in the first part of the paper the feasible filippov solution concept is introduced by characterizing single mode caratheodory sliding mode and forward zeno behaviors then a global asymptotic stability result through a possibly discontinuous piecewise lyapunov function is presented the sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing unreachable and caratheodory boundaries it is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic lyapunov functions and using the cone copositivity approach several examples illustrate the theoretical arguments and the effectiveness of the stability result

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

brief stability preserving interpolation methods for the synthesis of gain scheduled controllers synthesis of gain scheduled controllers for nonlinear plants often requires that a parameter varying controller be generated from a finite set of linear time invariant controllers we propose interpolation methods for this task with the property that stability of the linearized closed loop system is preserved for all values of the scheduling parameter in addition slow variation arguments are presented that establish local stability of the nonlinear closed loop system with gain scheduled controller

copositive lyapunov functions for switched systems over cones abstract we answer two open questions on copositive lyapunov functions which were recently posed by m k camlibel and j m schumacher in the book unsolved problems in mathematical systems and control theory edited by v d blondel and a megretski m k camlibel j m schumacher copositive lyapunov functions in v d blondel a megretski eds unsolved problems in mathematical systems and control theory princeton university press 2004 pp 189 193 available online at http press princeton edu math blondel these questions are what are necessary and sufficient conditions for the existence of a lyapunov function for a linear system which is defined over a cone how can this be extended to switched linear systems where the system matrix varies over time we present conditions answering these questions our conditions amount to checking feasibility or infeasibility of a system of linear inequalities

robust stability analysis of nonlinear hybrid systems we present a methodology for robust stability analysis of nonlinear hybrid systems through the algorithmic construction of polynomial and piecewise polynomial lyapunov like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials several improvements compared to previous approaches are discussed such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

robustness of discrete time adaptive controllers an input output approach a general input output approach that can be used for the design and analysis of robust discrete time adaptive control schemes is presented in particular a model reference adaptive controller is considered the design approach involves the use of the certainty equivalence principle to combine a robust control structure with a robust adaptive law using exponentially weighted i sub 2 norms and exploiting the properties of the adaptive law and the control structure robust stability is established for the closed loop adaptive control scheme

existence of solutions for a quasilinear schrodinger equation with subcritical nonlinearities abstract in this paper we consider the existence of solutions for the quasilinear schrodinger equation u v x u u 2 u g x u in r n where n 3 and g x u is a superlinear but subcritical function under periodic or asymptotically periodic assumptions on the nonlinearities we prove the existence of bounded states for this equation by the mountain pass theorem

technical communique relaxing pwq lyapunov stability criteria for pwa systems the note addresses the calculation of piecewise quadratic pwq lyapunov functions for pwa piecewise affine systems new lmi relaxations are proposed these relaxations have been found to be effective in cases where the traditional relaxations fail

nodal soliton solutions for quasilinear schrodinger equations with critical exponent this paper is concerned with constructing nodal radial solutions for quasilinear schrodinger equations in rn with critical growth which have appeared as several models in mathematical physics for any given integer k 0 by using a change of variables and minimization argument we obtain a sign changing minimizer with k nodes of a minimization problem since the critical exponent appears and the lower order term may change sign we should use more delicate arguments

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

global existence of small solutions to a relativistic nonlinear schrodinger equation on etudie le probleme de cauchy associea une equation de schrodinger non lineaire modelisant une impulsion laser ultra intense et ultra courte dans un plasma les termes non lineaires nouveaux sont dus aux effets relativistes et a la force ponderomotrice nous prouvons l existence locale et l unicite de solutions petites lorsque la dimension de l espace transverse est egale a 2 ou 3 ainsi que l existence locale pour des donnees initiales de taille arbitraire en dimension un d espace transverse

lyapunov stability for piecewise affine systems via cone copositivity cone copositive piecewise quadratic lyapunov functions pwq lfs for the stability analysis of continuous time piecewise affine pwa systems are proposed the state space is assumed to be partitioned into a finite number of convex possibly unbounded polyhedra preliminary conditions on pwq functions for their sign in the polyhedra and continuity over the common boundaries are provided the sign of each quadratic function is studied by means of cone constrained matrix inequalities which are translated into linear matrix inequalities lmis via cone copositivity the continuity is guaranteed by adding equality constraints over the polyhedra intersections an asymptotic stability result for pwa systems is then obtained by finding a continuous pwq lf through the solution of a set of constrained lmis the effectiveness of the proposed approach is shown by analyzing an opinion dynamics model and two saturating control systems

brief hysteresis based switching algorithms for supervisory control of uncertain systems we address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers we present a new hysteresis based switching logic designed specifically for this purpose and derive a bound on the number of switches produced by this logic on an arbitrary time interval the resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

periodic and asymptotically periodic quasilinear elliptic systems in this work we are concerned with the existence and nonexistence of ground state solutions for the following class of quasilinear schrodinger coupled systems taking into account periodic or asymptotically periodic potentials the nonlinear terms are superlinear at infinity and at the origin by using a change of variable we turn the quasilinear system into a nonlinear system where we can establish a variational approach with a fine analysis on the nehari method for the nonexistence result we compare the potentials with periodic potentials proving the nonexistence of ground state solutions

interpolation of observer state feedback controllers for gain scheduling the authors propose a method of interpolating linear time invariant controllers with observer state feedback structure in order to generate a continuously varying family of controllers that stabilizes a family of linear plants gain scheduling is a motivation for this work and the interpolation method yields guidelines for the design of gain scheduled controllers the method is illustrated with the design of a missile autopilot using loop shaping h infinity controllers

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9

existence of solution for a generalized quasilinear elliptic problem it establishes existence and multiplicity of solutions to the elliptic quasilinear schrodinger equation div g2 u u g u g u u 2 v x u h x u x n where g h v are suitable smooth functions the function g is asymptotically linear at infinity and for each fixed x n the function h x s behaves like s at the origin and s3 at infinity in the proofs we apply variational methods