generalized invariant subspaces and parameter insensitive disturbance rejection problems with static output feedback in the geometric approach some generalized invariant subspaces for uncertain linear systems are investigated and then various parameter insensitive disturbance rejection problems with static output feedback are formulated and necessary and sufficient conditions for the problems to be solvable are presented further some sufficient conditions which are useful to check the solvability conditions are presented using the notions of generalized invariant subspaces

generalized invariant subspaces for infinite dimensional systems in this paper some generalized invariant subspaces for infinite dimensional systems are investigated and then some sufficient conditions for parameter insensitive disturbance rejection problems with state feedback and with measurement output feedback to be solvable are studied

improved generalized quasilinearization method and rapid convergence for reaction diffusion equations abstract in the method of quasilinearization or the method of generalized quasilinearization we assume that k f t x u u k exists where f t x u is the forcing function and obtain kth order of convergence in this paper we assume a weaker condition namely k 1 f t x u u k 1 exists and lipschitzian in u and develop generalized quasilinearization method to reaction diffusion equations the iterates will be different depending on k 1 f t x u u k 1 is nondecreasing or nonincreasing in u and k being even or odd finally we prove that the sequences generated by the generalized quasilinearization method converge to the unique solution of the nonlinear reaction diffusion equation and the convergence is of order k

brief paper state feedback stabilization of linear impulsive systems we address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily spaced impulse times and possibly singular state transition matrices specifically we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed loop system the approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well known results for time varying linear systems for both continuous and discrete time cases

multiple positive solutions of second order differential equations abstract in this paper by using the coincidence degree method we obtain some sufficient conditions for the existence of multiple positive periodic solutions of a class of second order differential equations under the existence of upper and lower solutions

a necessary and sufficient condition for parameter insensitive disturbance rejection problem with state feedback in this paper a necessary and sufficient condition for a parameter insensitive disturbance rejection problem with state feedback which was pointed out as an open problem by bhattacharyya to be solvable is proved a constructive algorithm of simultaneously a b invariant subspaces for a finite number of linear systems and a relationship between simultaneously a b invariant subspaces and generalized a b invariant subspaces play an important role to prove the main result

multiple periodic solutions of a class of p laplacian by using the recent generalization of coincidence degree method the existence of multiple periodic solutions for a class of p laplacian is obtained under the existence of strict upper and lower solutions

generalized quasilinearization method for mixed boundary value problems a generalized quasilinearization method for a nonlinear mixed bvp is developed and a sequence of approximate solutions converging monotonically and quadratically to a solution of the given problem is presented

model matching with strong stability in switched linear systems abstract this work deals with model matching by output dynamic feedback in switched linear systems the plant and the model are assumed to be subject to different switching signals a necessary and sufficient condition for achieving model matching with asymptotic stability of both the closed loop compensated system and the compensator for a sufficiently large dwell time is proven such condition is obtained by specializing the structural condition with a suitable redefinition of the robust controlled invariant subspace involved capable of capturing not only the structural aspect of the problem but also the stability aspects the effect of the combined action of nonzero initial states and nonzero inputs is dealt with the solution to a more demanding problem formulation where the dwell time is assumed to be fixed and given is also discussed

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

representation of integral dispersion relations by local forms the representation of the usual integral dispersion relations idrs of scattering theory through series of derivatives of the amplitudes is discussed extended simplified and confirmed as mathematical identities forms of derivative dispersion relations ddrs valid for the whole energy interval recently obtained and presented as double infinite series are simplified through the use of new sum rules of the incomplete functions being reduced to single summations where the usual convergence criteria are easily applied for the forms of the imaginary amplitude used in phenomenology of hadronic scattering at high energies we show that expressions for the ddr can represent with absolute accuracy the idr of scattering theory as true mathematical identities besides the fact that the algebraic manipulation can be easily understood numerical examples show the accuracy of these representations up to the maximum available machine precision as consequence of our work it is concluded that the standard

stability and boldsymbol l_ 1 gain analysis for positive takagi sugeno fuzzy systems with impulse this paper is concerned with the stability analysis and l 1 gain characterization for positive takagi sugeno fuzzy systems subject to impulse effects the main tool utilized is the construction of an impulse time dependent discretized copositive lyapunov function where the impulse interval partitioning idea is exploited to derive less conservative results for the disturbance free case stability criteria are developed to guarantee global exponential stability of the concerned systems under ranged and constant dwell time constraints the analysis of the influence of the discretizing parameter on the reduction of conservativeness is performed we further employ the proposed impulse time dependent discretized copositive lyapunov function to analyze the l 1 gain performance for the case where external disturbances are considered by performing a grid search for a scalar in an interval all the proposed criteria can be checked via linear programming finally numerical simulations are discussed to illustrate the effectiveness of the theoretical results

a quasilinearization method for second order four point boundary value problems abstract in this paper we obtain the existence and uniqueness results for general second order four point boundary value problems by applying the method of upper and lower solutions together with leray schauder degree also we obtain monotone iteration schemes which converge quadratically to the unique solution of some specific second order four point boundary value problems by using the method of quasilinearization

disturbance decoupling in hybrid linear systems with state jumps this work investigates the problem of making the output of a hybrid linear system totally insensitive to a disturbance input while attaining global asymptotic stability of the compensated hybrid dynamics in the presence of possibly nonuniformly spaced state jumps meeting the only condition that the minimum time between two consecutive occurrences is no smaller than a given positive real constant both existential and constructive necessary and sufficient conditions for solvability of the problem addressed are proven

simultaneous c a b pairs for infinite dimensional systems abstract in this paper the infinite dimensional version of the simultaneous c a b pair is introduced and its properties are investigated and robust disturbance rejection problem with dynamic compensator is formulated and then its solvability conditions are presented

disturbance decoupling by measurement feedback with stability for infinite dimensional systems the concepts of controllability and stabilizability subspaces are extended to infinite dimensional linear systems under certain assumptions one obtains a nice generalization of the finite dimensional theory and by dualizing similar results are obtained for the concepts of complementary observability and complementary detectability subspaces these concepts are used to solve the infinite dimensional version of the disturbance decoupling problem the disturbance decoupled estimation problem and the disturbance decoupling problem with measurement feedback all requiring various stability requirements the solution is in terms of geometric concepts such as a b and c a invariant subspaces and controllability and complementary observability subspaces

generalized controlled and conditioned invariances for linear ω periodic discrete time systems abstract in this paper the three notions of generalized controlled a b invariance generalized conditioned c a invariance and generalized a b c invariance for uncertain linear periodic discrete time systems are studied and then the parameter insensitive disturbance rejection problems with static output feedback and or with state feedback are formulated and their solvability conditions are presented

hybrid output regulation for linear systems with periodic jumps solvability conditions structural implications and semi classical solutions the problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper necessary and sufficient conditions for its solution are provided both in the full information and error feedback case by a detailed analysis of such conditions several interesting properties are derived including the fact that the regulator must contain a suitably defined copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics and the fact that the output regulation problem is generically solvable for fat plants having more inputs than outputs and generically not solvable for square plants in addition semi classical solutions to the hybrid output regulation problem are introduced and discussed such solutions are characterized by the property that the required steady state input can be generated as a simple linear function of the state of the exosystem as in the non hybrid case although the associated steady state response has a genuinely hybrid structure

the geometric approach for linear periodic discrete time systems abstract recently the disturbance localization problem and the problems of designing disturbance decoupled observers and of giving a geometric characterization of invariant zeros were solved for linear periodic discrete time systems through an extension of the geometric approach based on the notions of controlled invariant and conditionally invariant subspaces to periodic ones here the existing periodic geometric theory is supplemented with the notions of outer reachable subspace and controllability subspace and with some further results on the previously introduced notions of inner reachable controllable subspace and outer controllable subspace in addition it is shown that any such periodic geometric theory can be restated in an equivalent time invariant form which is just the same theory written for a suitable time invariant system having an extended state space

the output regulation problem with stability for linear switching systems a geometric approach abstract this work presents a solution for the output regulation problem with quadratic stability under arbitrary switching in linear switching systems the extension to other stability requirements like asymptotic stability in particular is also considered and it is shown to affect only few specific features of the proposed solution the main reason is that the geometric approach which is at the basis of the developed methodology establishes a neat separation between the structural aspects and the stability aspects of the problem for the same reason continuous time systems and discrete time systems are given a unified treatment as far as the structural issues are concerned while different technicalities characterize the discussion of the stability issues

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

the quasilinearization method for boundary value problems on time scales abstract in this paper we apply the method of quasilinearization to a family of boundary value problems for second order dynamic equations y q t y h t y on time scales the results include a variety of possible cases when h is either convex or a splitting of convex and concave parts and whether lower and upper solutions are of natural form or of natural coupled form

on the validity and practical applicability of derivative analyticity relations we examine derivative analyticity relations dar which were originally proposed by bronzan as an alternative to dispersion relations and in which the dispersion integral is replaced by a tangent series of derivatives we characterize the class of functions satisfying dar and show that outside this class the dispersion integral represents a borel like sum of tangent series we point out difficulties connected with the application of dar

disturbance decoupling with quadratic stability for switched linear systems in this paper disturbance decoupling problems without stability and with quadratic stability for switched linear systems are formulated in the framework of the so called geometric approach firstly necessary and sufficient conditions for the problem without stability to be solvable are given secondly sufficient conditions for the problem with quadratic stability to be solvable are given further for switched linear systems composed of two subsystems necessary and sufficient conditions for the problem with quadratic stability to be solvable are also investigated finally an illustrative example is shown

the method of quasilinearization and dynamic equations on compact measure chains the method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand in this paper we show the method applies to a family of two point boundary value problems for a dynamic equation on a compact measure chain

two point derivative dispersion relations a new derivation is given for the representation under certain conditions of the integral dispersion relations of scattering theory through local forms the resulting expressions have been obtained through an independent procedure to construct the real part and consist of new mathematical structures of double infinite summations of derivatives in this new form the derivatives are calculated at the generic value of the energy e and separately at the reference point e m that is the lower limit of the integration this new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard derivative dispersion relations ddr for all cases in which the reductions of the double to single sums were obtained in our previous work leading to explicit demonstration of convergence these new expressions are seen to be identical to the previous ones we present as a glossary the most simplified e