invertibility and inversion of linear periodic systems abstract in this paper the invertibility properties of periodic discrete time systems are studied necessary and sufficient conditions for the existence and a synthesis procedure for constructing left and right inverses are given

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

control of linear discrete time periodic systems a decentralized control approach a decentralized control technique is applied to the problem of periodic output feedback stabilization or pole assignment for a periodically time varying discrete time system it is shown that the problem can be reduced to that of stabilizing or pole assigning a general proper multichannel system by static output feedback on the basis of the equivalence between periodic systems and a class of linear time invariant systems the notion of periodic fixed mode is introduced for a periodic system similar to the notion of uncontrollable or unobservable modes in terms of this notion both necessary conditions and sufficient conditions for the solvability of the problem are obtained

on some norm equalities in pre hilbert c modules abstract we characterize when the norm of the sum of two elements in a pre hilbert c module equals the sum of their norms we also give the necessary and sufficient conditions for two orthogonal elements of a pre hilbert c module to satisfy pythagoras equality

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

on the gain margin improvement using dynamic compensation based on generalized sampled data hold functions this paper shows that the use of dynamic compensation based on generalized sampled data hold functions gshf can arbitrarily improve the gain margin for continuous time nonminimum phase linear systems the gshf compensator is a particular periodic digital controller the effect of sampling period on the gain margin is analyzed furthermore it is proved that under a mild condition the gain margin improvement can be achieved without forcing the sampling period small an important advantage of periodic compensation over lti compensation is found to be the capability of reducing conflict between gain margin and sensitivity

analysis of the periodic lyapunov and riccati equations via canonical decomposition a new proof is given of the following result a periodic riccati equation admits a unique positive semidefinite periodic solution and the solution is stabilizing if and only if the underlying system is stabilizable and detectable the proof hinges on the decomposition of the riccati equation induced by the system canonical decomposition the solution structure is therefore naturally pointed out

relative controllability of fractional delay differential equations via delayed perturbation of mittag leffler functions abstract this paper is concerned with the relative controllability of fractional delay systems in control for finite dimensional spaces a notion of fractional delay grammian matrix involving two parameter mittag leffler type delay matrix function is introduced sufficient and necessary condition is established to examine that linear system is relatively controllable controllability result for semilinear system is obtained by krasnoselskii s fixed point theorem examples are given to illustrate theoretically results

multivariable multirate sampled data systems state space description transfer characteristics and nyquist criterion first a discrete time state space description is derived for multivariable multirate sampled data systems then the multirate impulse modulation mim and the symmetric coordinate multirate impulse modulation smim of a transfer matrix are defined and their relation to the discrete time state space description is clarified based on the above results four stability criteria are derived the contents of the paper will be useful to extend the modern results about continuous time and single rate sampled data control systems to the multirate sampled data case especially extensions of the ina method and of the robust stability conditions will be straightforward

controllability of linear discrete systems with constant coefficients and pure delay the purpose of this contribution is to develop a controllability method for linear discrete systems with constant coefficients and with pure delay to do this a representation of solutions with the aid of a discrete matrix delayed exponential is used such an approach leads to new conditions of controllability except for a criterion of relative controllability a control function is constructed as well

the dunkl williams equality in pre hilbert c modules in this paper we consider the case of equality in some generalizations of the dunkl williams inequality for elements of a pre hilbert c module

disturbance localization for left invertible linear periodic discrete time systems the disturbance localization problem for left invertible linear periodic discrete time systems is solved using periodic state feedback controllers the proposed technique is of algebraic nature and has the following two main characteristics i it yields simple algebraic criteria for testing the solvability of the problem as compared to known geometric criteria which may not be so easy to check ii it derives analytically the general expressions of all periodic controllers admissible for disturbance localization as compared to known techniques which lead to nonanalytic parametrizations of the admissible controllers via constructive procedures moreover for the aforementioned class of periodic systems the state feedback simultaneous disturbance localization and stabilization or pole placement problem is treated and conditions for its solvability are established on the basis of a decentralized control approach that makes use of the equivalence between the above problem and the stabilization or pole placement problem of a general proper multichannel system by decentralized static output feedback

pole assignment for linear time invariant systems by periodic memoryless output feedback it is well known that the poles of a linear time invariant controllable and observable system can be assigned arbitrarily by state feedback when only the output is available pole assignment is still possible by means of dynamic output feedback in this paper the potential of time varying memoryless output feedback is considered it is shown that up to some technical conditions it is indeed possible to allocate the poles of a linear time invariant discrete time system by memoryless output feedback with periodic gains the period of the gains is n 1 with n the order of the system the power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach

norm equalities in pre hilbert c modules abstract we discuss the connection between the equality case in the triangle inequality for two elements x and y in a pre hilbert module e over the c algebra a and the equality case in the corresponding cauchy schwarz inequality we firstly show that the triangle equality associated to the rank one operators x x and y y holds true if and only if x y a x y the special situations when x y is a perturbation by a scalar of an idempotent x y x y iff x y 1 1 2 or it has positive real part x y x y iff r x y a x y are also considered in the last part we characterize pythagoras equality in pre hilbert c modules our results extend or improve some theorems due to l arambasic and r rajic

geometric and algebraic structure at infinity of discrete time linear periodic systems a notion of structure at infinity for linear discrete time periodic system is proposed and investigated in particular two equivalent characterizations of such notion are given a geometric one and an algebraic one the first is based on an extension to the periodic case of the controlled invariant subspace algorithm and the second is based on a newly developed periodic version of the structure algorithm an application to a model matching problem is described

characterization of equality in a generalized dunkl williams inequality abstract we establish a generalization of the dunkl williams inequality and its inverse in the framework of hilbert c modules and characterize the equality case as applications we get some new results and some known results due to j e pecaric and r rajic the dunkl williams equality in pre hilbert c modules linear algebra appl 425 1 2007 16 25

robust tracking and regulation of linear periodic discrete time systems in this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete time systems and for general classes of disturbance functions and reference signals consisting in free responses of periodic processes the necessary and sufficient conditions for the existence of a solution which involve the periodic notion of invariant zero are found a constructive design procedure of the periodic compensator is given it is based on the internal model principle

stability switches in linear delay difference equations the paper discusses necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear delay difference equation y n 1 email protected n email protected n k where a b are complex numbers and k is a positive integer compared to the case when a b are real numbers the stability behavior of this equation turns out to be much richer in particular if a b 1 then as k monotonously increases the equation may switch finite times from asymptotic stability to instability and vice versa we describe an interesting structure of the set of these stability switches their explicit values and apply the obtained results to some important delay difference equations and their systems

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

stability and exponential stability of linear discrete systems with constant coefficients and single delay this paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x k 1 a x k b x k m k 0 1 where a b are square constant matrices and m n sufficient conditions for exponential stability are derived using the method of lyapunov functions and its efficiency is demonstrated by examples

decentralized control of multi channel systems with direct control feedthrough abstract linear time invariant multi channel general proper systems with direct control feedthrough are considered a polynomial matrix method is presented to derive explicit conditions characterizing the systems which can be made controllable or stabilizable through a single channel by applying non dynamic decentralized feedback to all other channels these conditions are then applied to the decen tralized pole assignment and stabilization problems for the systems yielding a complete criterion for determining when the closed loop spectrum can be freely assigned or stabilized with decentralized control it can be expected that the results obtained will have direct application to periodic discrete time control systems

exploring delayed mittag leffler type matrix functions to study finite time stability of fractional delay differential equations abstract in this paper we introduce a concept of delayed two parameters mittag leffler type matrix function which is an extension of the classical mittag leffler matrix function with the help of the delayed two parameters mittag leffler type matrix function we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method in addition we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations thereafter we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term finally an example is presented to illustrate the validity of the main theorems

the birkhoff james orthogonality in hilbert c modules abstract in this paper we characterize the birkhoff james orthogonality for elements of a hilbert c module in terms of states of the underlying c algebra we also show that the birkhoff james orthogonality in a hilbert c module over a c algebra a and orthogonality with respect to the a valued inner product coincide if and only if a is isomorphic to c in addition some new results concerning the case of equality in the triangle inequality for elements of a hilbert c module are obtained

representation of solutions of delayed difference equations with linear parts given by pairwise permutable matrices via z transform in the present paper a system of nonhomogeneous linear difference equations with any finite number of constant delays and linear parts given by pairwise permutable matrices is considered representation of its solution is derived in a form of a matrix polynomial using the z transform so the recent results for one and two delays and an inductive formula for multiple delays are unified the representation is suitable for theoretical as well as practical computations

pole assignment for linear periodic systems by memoryless output feedback we consider linear periodic discrete time systems we are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period it is well known that in general the poles of time invariant systems cannot be assigned by constant output feedback this is in contrast with what can be obtained in the context of time variant systems the main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems