global stabilization of linear discrete time systems with bounded feedback abstract this paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws the main result proved is an analog of one proved for the continuous time case by the authors and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one the proof provides in principle an algorithm for the construction of such feedback laws which can be implemented either as cascades or as parallel connections single hidden layer neural networks of simple saturation functions

finite gain l sub p stabilization of discrete time linearsystems subject to actuator saturation the case of p 1 it has been established by bao lin and sontag 2000 that for neutrally stable discrete time linear systems subject to actuator saturation finite gain l sub p stabilization can be achieved by linear output feedback for every p spl isin 1 spl infin except p 1 an explicit construction of the corresponding feedback laws was given the feedback laws constructed also resulted in a closed loop system that is globally asymptotically stable this note complements the results of bao lin and sontag 2000 by showing that they also hold for the case of p 1 in establishing our results for p 1 we also allow the presence of certain additional external disturbance

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

constrained stabilization problems for linear plants linear systems with magnitude and rate constraints on both the state and control variables are considered for such systems semi global and global constrained stabilization problems are formulated when state feedback controllers are used necessary and sufficient conditions for the solvability of the formulated problems are developed moreover design methodologies for such constrained stabilization problems are presented an important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

simultaneous global external and internal stabilization of linear time invariant discrete time systems subject to actuator saturation simultaneous external and internal stabilization in a global framework for linear time invariant discrete time systems subject to actuator saturation is considered internal stabilization is in the sense of lyapunov while external stabilization is in the sense of p stability with different variations e g with or without finite gain with fixed or arbitrary initial conditions with or without bias several simultaneous external and internal stabilization problems all in the global framework are studied in depth moreover we present a design for appropriate adaptive low and high gain feedback controllers that achieve the intended simultaneous external and internal stabilization whenever such problems are solvable

semi global stabilizability of linear null controllable systems with input nonlinearities an h sub spl infin based lyapunov proof is provided for a result established by lin and saberi 1993 if a linear system is asymptotically null controllable with bounded controls then when subject to input saturation it is semi globally stabilizable by linear state feedback a new result is that if the system is also detectable then it is semi global stabilizable by completely linear output feedback further an extension which relaxes the requirements on the input characteristic is obtained

brief finite gain stabilization of discrete time linear systems subject to actuator saturation it is shown that for neutrally stable discrete time linear systems subject to actuator saturation finite gain l p stabilization can be achieved by linear output feedback for all p 1 an explicit construction of the corresponding feedback laws is given the feedback laws constructed also result in a closed loop system that is globally asymptotically stable and in an input to state estimate

the uniform measure of simple regular sets of infinite trees abstract we consider the problem of computing the measure of a regular set of infinite binary trees while the general case remains unsolved we show that the measure of a language can be computed when the set is given in one of the following three formalisms a first order formula with no descendant relation a boolean combination of conjunctive queries with descendant relation or by a non deterministic safety tree automaton additionally in the first two cases the measure of the set is always rational while in the third it is an algebraic number moreover we provide an example of a first order formula that uses descendant relation and defines a language of infinite trees having an irrational but algebraic measure

doubly slice knots and the casson gordon invariants we find knots in all dimensions which are algebraically but not geometri cally doubly slice our new obstructions involve the casson gordon invariants of the finite cyclic covers in odd dimensions and of the infinite cyclic cover in even dimensions these same invariants provide new criteria for amphicheirality and invertibility of even dimensional knots

h sub spl infin almost disturbance decoupling with internal stability for linear systems subject to input saturation for a linear system subject to input saturation and input additive disturbances we show that 1 the h sub spl infin almost disturbance decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system in the absence of saturation is stabilizable no matter where the open loop poles are and 2 the h sub spl infin almost disturbance decoupling problem with semiglobal asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left half plane the results generalize those in lin et al 1996 by not requiring the disturbance to be bounded by a known bound or even bounded

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

output regulation for linear systems subject to input saturation the purpose of this paper is to examine the problem of controlling a linear time invariant system subject to input saturation in order to have its output track or reject a family of reference or disturbance signals produced by some external generator it is shown that a semiglobal framework for this problem is a natural one within this framework a set of solvability conditions are given and feedback laws that solve the problem are constructed the theory developed in this paper incorporates earlier results established for linear systems without input saturation

a parametric lyapunov equation approach to the design of low gain feedback low gain feedback has found several applications in constrained control systems robust control and nonlinear control low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic riccati equation are the eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter while the are approach requires the solution of an are for each value of the parameter this note proposes an alternative approach to low gain feedback design based on the solution of a parametric lyapunov equation such an approach possesses the advantages of both the eigenstructure assignment approach and the are based approach it also avoids the possible numerical stiffness in solving a parametric are and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

holomorphic triangles and invariants for smooth four manifolds abstract in earlier articles the authors introduced invariants for closed oriented three manifolds defined using a variant of lagrangian floer homology in the symmetric products of riemann surfaces the aim of this article is to introduce invariants of oriented smooth four manifolds built using these floer homology groups this four dimensional theory also endows the corresponding three dimensional theories with additional structure an absolute grading of certain of its floer homology groups

brief paper a parametric lyapunov equation approach to low gain feedback design for discrete time systems low gain feedback a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has found several applications in constrained control systems robust control and nonlinear control in the continuous time setting there are currently three ways of constructing low gain feedback laws the eigenstructure assignment approach the parametric are based approach and the parametric lyapunov equation based approach the eigenstructure assignment approach leads to feedback gains explicitly parameterized in the low gain parameter the parametric are based approach results in a lyapunov function along with the feedback gain but requires the solution of an are for each value of the parameter the parametric lyapunov equation based approach possesses the advantages of the first two approaches and results in both an explicitly parameterized feedback gains and a lyapunov function the first two approaches have been extended to discrete time setting this paper develops the parametric lyapunov equation based approach to low gain feedback design for discrete time systems

impulsive synchronization of discrete time networked oscillators with partial input saturation abstract in this paper a novel impulsive control with partial input saturation is proposed to synchronize a class of discrete time delayed coupled networks the proposed impulsive control with partial input saturation means that the considered impulsive controllers are subject to input saturation and only a fraction of nodes are injected with controllers for this purpose the razumikhin type technique and mathematical induction are utilized to derive a sufficient criterion in addition the control gains are calculated by transforming the criterion into a convex optimization problem finally the result is verified through numerical simulation