global stabilization and restricted tracking with bounded feedback for multiple oscillator systems this paper is concerned with the problems of global stabilization and restricted tracking for a multiple oscillator system by bounded feedback a nonlinear feedback law consisting of nested saturation functions is proposed to achieve global stabilization to improve the transient performance of the closed loop system the parameters in this feedback law can be tuned to assign the poles of the closed loop system when none of the saturation elements in the control law is in effect the proposed feedback law is also shown to achieve restricted tracking simulation results are given to show the effectiveness of the proposed feedback law

technical communique semi global stabilization of linear time delay systems with control energy constraint this note is concerned with the problem of semi globally stabilizing a linear system with an input delay and a constraint on the energy of its input under the condition of null controllability with vanishing energy the parametric lyapunov equation based l 2 low gain feedback is adopted to solve the problem the proposed approach is applied to the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another spacecraft in a circular orbit around the earth to validate its effectiveness

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

linear systems subject to input saturation and time delay global asymptotic stabilization this note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay under standard necessary conditions we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large constant delay to validate the approach a third order integrator and oscillator with multiplicity two example is presented

l_p stabilization of integrator chains subject to input saturation using lyapunov based homogeneous design consider the n th integrator dot x j nx sigma u e n where x in mathbb r n u in mathbb r j n is the n th jordan block and e n 0 cdots 0 1 t in mathbb r n we provide easily implementable state feedback laws u k x which not only render the closed loop system globally asymptotically stable but also are finite gain l p stabilizing with arbitrarily small gain as in a saberi p hou and a stoorvogel ieee trans automat control 45 2000 pp 1042 1052 these l p stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite time stabilization of linear systems we also provide additional l infty stabilization results for the case of both internal and external disturbances of the n th integrator namely for the perturbed system dot x j nx e n sigma k x d d where d in mathbb r and d in mathbb r n

matrix transformations between the sequence spaces w 0 p λ v 0 p λ c 0 p λ 1 p and certain bk spaces in this paper we determine the b duals of the sets w 0 p l v 0 p l and c 0 p l for exponentially bounded email protected furthermore we characterize matrix transformations between the sequence spaces w 0 p l v 0 p l c 0 p l 1

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

tacnode gue minor processes and double aztec diamonds we study determinantal point processes arising in random domino tilings of a double aztec diamond a region consisting of two overlapping aztec diamonds at a turning point in a single aztec diamond where the disordered region touches the boundary the natural limiting process is the gue minor process increasing the size of a double aztec diamond while keeping the overlap between the two aztec diamonds finite we obtain a new determinantal point process which we call the tacnode gue minor process this process can be thought of as two colliding gue minor processes as part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode gue minor process we find the inverse kasteleyn matrix for the dimer model version of the double aztec diamond

compactness of matrix operators on some new difference sequence spaces abstract the difference sequence spaces c 0 and l have recently been introduced by mursaleen and noman 2010 m mursaleen a k noman on some new difference sequence spaces of non absolute type math comput modelling 52 3 4 2010 603 617 in the present paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on the spaces c 0 and l further by using the hausdorff measure of noncompactness we characterize some classes of compact operators on these spaces

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

a circle criterion for strong integral input to state stability abstract we present sufficient conditions for integral input to state stability iiss and strong iiss of the zero equilibrium pair of continuous time forced lur e systems where by strong iiss we mean the conjunction of iiss and small signal iss our main results are reminiscent of the complex aizerman conjecture and the well known circle criterion we derive a number of corollaries including a result on stabilisation by static feedback in the presence of input saturation in particular we identify classes of forced lur e systems with saturating nonlinearities which are strongly iiss but not iss

compact operators on the spaces a0r δ and acr δ abstract in c aydin f basar some new difference sequence spaces appl math comput 157 2004 677 693 aydin and basar introduced the new difference sequence spaces a c r and a 0 r and characterized the classes a c r l p and a c r c here we characterize the subclasses k x y of compact operators where x is a c r and y is one of the spaces c 0 c l l 1 b v by applying the hausdorff measure of noncompactness

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

robust stabilization via saturated feedback in this paper we deal with the problem of stabilization of uncertain systems in the presence of input constraint first algebraic conditions are derived for input to state stability of linear system with saturated linear feedback of low dimension then a recursive design procedure is derived for robust stabilization of block upper triangular nonlinear systems with feedforward structure

some new difference sequence spaces the difference sequence spaces d c d and c 0 d were studied by kizmaz canad math bull 24 2 1981 169 the sequence spaces a 0 r and a c r have been recently defined and examined by aydin and basar in hokkaido math j in press the main purpose of the present paper is to introduce the spaces a r 0 d and a r c d of difference sequences moreover it is proved that the spaces a r 0 d and a r c d are the bk spaces including the spaces c 0 and c and some inclusion relations have been given it is also proved that the sequence space a 0 r has ad property while the space a 0 r d has not furthermore the basis and the a b and c duals of the spaces a r 0 d and a r c d have been determined the last section of the paper has been devoted to theorems on the characterizations of the matrix classes a r c d p and a r c d c and the characterizations of some other matrix classes have been obtained by means of a given basic lemma where 1

a note on compact operators on matrix domains abstract we establish some identities or estimates for the operator norms and hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary bk spaces with ak or in the spaces of all convergent or bounded sequences into the spaces of all null convergent or bounded sequences or of all absolutely convergent series furthermore we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces and on the sequence spaces studied in i djolovic compact operators on the spaces a 0 r and a c r j math anal appl 318 2 2006 658 666 i djolovic on the space of bounded euler difference sequences and some classes of compact operators appl math comput 182 2 2006 1803 1811

brief paper disturbance tolerance and rejection of linear systems with imprecise knowledge of actuator input output characteristics we study the robustness of linear systems with respect to the disturbances and the uncertainties in the actuator input output characteristics disturbances either bounded in energy or bounded in magnitude are considered the actuator input output characteristics are assumed to reside in a so called generalized sector bounded by piecewise linear curves robust bounded state stability of the closed loop system is first defined and characterized in terms of linear matrix inequalities lmis based on this characterization the evaluation of the disturbance tolerance and disturbance rejection capabilities of the closed loop system under a given feedback law is formulated into and solved as optimization problems with lmi constraints

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

further constructions of control lyapunov functions and stabilizing feedbacks for systems satisfying the jurdjevic quinn conditions for a broad class of nonlinear systems we construct smooth control lyapunov functions we assume our systems satisfy appropriate generalizations of the jurdjevic quinn conditions we also design state feedbacks of arbitrarily small norm that render our systems integral input to state stable to actuator errors

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

measure of noncompactness of matrix operators on some difference sequence spaces of weighted means for a sequence x x k we denote the difference sequence by dx x k x k 1 let u u k k 0 and v v k k 0 be the sequences of real numbers such that u k 0 v k 0 for all email protected n the difference sequence spaces of weighted means l u v d are defined as l u v d x x k w x email protected where l c c 0 and and the matrix w w n k is defined by w n k u n v k v k 1 kn in this paper we establish some identities or estimates for the operator norms and the hausdorff measures of noncompactness of certain matrix operators on l u v d further we characterize some classes of compact operators on these spaces by using the hausdorff measure of noncompactness

on matrix domains of triangles we prove some general results for the determination of the duals of and the characterisations of matrix transformations on matrix domains of arbitrary triangles in fk spaces our results contain almost all recently published ones as special cases we also study the measure of noncompactness of several matrix transformations in particular we obtain some known results of sember give the corrected version of a recent result by djolovic and study compact operators on some spaces of altay basar and mursaleen

global asymptotic controllability implies input to state stabilization the main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable gac control affine systems that render the closed loop systems input to state stable iss with respect to actuator errors extensions for fully nonlinear gac systems with actuator errors are also discussed our controllers have the property that they tolerate small observation noise as well

spl lambda sub 2 gain of double integrators with saturation nonlinearity this note uses quadratic surface lyapunov functions sulfs to efficiently check if a double integrator in feedback with a saturation nonlinearity has l 2 gain less than 0 we show that for many such systems the l 2 gain is nonconservative in the sense that this is approximately equal to the lower bound obtained by replacing the saturation with a constant gain of 1 these results allow the use of classical analysis tools like analysis or integral quadratic constraints to analyze systems with double integrators and saturations including servo systems like some mechanical systems satellites hard disks compact disk players etc

on the space of bounded euler difference sequences and some classes of compact operators abstract in this paper we consider the new one sequence space a r and characterize matrix transformations between a r and certain bk spaces further we define the subclasses of compact operators applying the hausdorff measure of noncompactness our results extend those in c aydin f basar some new difference sequence spaces appl math comput 157 2004 677 693 i djolovic compact operators on the spaces a 0 r and a c r j math anal appl 318 2006 658 666

brief input to state stability for a class of lurie systems we analyze input to state stability iss for the feedback interconnection of a linear block and a nonlinear element this study is of importance for establishing robustness against actuator nonlinearities and disturbances in the absolute stability framework we prove iss from a positive real property of the linear block by restricting the sector nonlinearity to grow unbounded as its argument tends to infinity when this growth condition is violated examples show that the iss property is lost the result is used to give a simple proof of boundedness for negative resistance oscillators such as the van der pol oscillator in a separate application we relax the minimum phase assumption of an earlier boundedness result for systems with nonlinearities that grow faster than linear