disturbance decoupling problems by measurements feedback a characterization of all solutions and fixed modes this paper presents a new approach to disturbance decoupling problems by measurement feedback ddpm the novelty in this approach is that it yields a characterization of the sets of all solutions to ddpm and ddpm with internal stability and that the set of fixed modes of ddpm with respect to dynamic output feedback is easily identified the central object used in deriving these results is a minimal polynomial basis of a rational vector space which conveniently represents the problem data

on disturbance decoupling in descriptor systems the disturbance decoupling problem for a linear multivariable control system is to determine when and how a state feedback may be chosen so that some class of disturbances has no effect on the system output the development of necessary and sufficient conditions for the solvability of this problem for state space systems by wonham and his co workers has profoundly influenced geometric control theory particularly by means of the concept of an a b invariant subspace this paper develops necessary and sufficient conditions for solvability of this problem for linear systems described by a mixture of algebraic and differential equations although the argument presented has the same structure as in the state space case and incorporates a generalisation of a b invariant subspaces to descriptor systems there are some additional issues demanding particularly careful attention is the ensuring of existence and uniqueness of classical solutions of the underlying differential equations which cannot be tak

disturbance rejection a polynomial approach a detailed analysis of the disturbance rejection problem in single input single output linear systems is presented the analysis is based on an external polynomial model and employs the algebra of polynomials all solutions are expressed in a parametric form and solvability conditions are given for a number of constraints including those of internal stability and arbitrary pole placement measurable and unmeasurable disturbances are distinguished and the effect of output feedback is investigated a simple design procedure is then proposed which provides a stable dynamical solution and which can be extended so as to minimize its order the procedure consists of solving two linear polynomial equations and yields the compensator in a compact form suitable for direct realization

disturbance rejection of left invertible systems abstract a new approach is presented for the study of the disturbance rejection of left invertible systems via proportional state feedback reducing the problem to that of solving a linear algebraic system of equations on the basis of this system of equations the necessary and sufficient conditions for the existence of a solution to the disturbance rejection problem are established in a form of simple algebraic criteria thus reducing the computational effort over known results and the general analytical expressions of all solutions of the controller matrices are derived these solutions are parameterized only by an arbitrary matrix

on the existence of homomorphisms between principal series representations of complex semisimple lie groups abstract we determine when there exists a nonzero homomorphism between principal series representations of a complex semisimple lie group we also determine the condition for the existence of nonzero homomorphisms between twisted verma modules

translation and shuffling of projectively presentable modules and a categorification of a parabolic hecke module translation and shuffling of projectively presentable modules and a categorification of the parabolic hecke module

frequency domain conditions for the solvability of the multivariable disturbance decoupling problem given a plant description in terms of its transfer matrices necessary and sufficient conditions are derived in the frequency domain for the solvability of the multivariable disturbance decoupling problem with independent controlled and measured outputs

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

observer design for generalized state space systems with unknown inputs abstract the following four major aspects for the observer design problem for generalized state space systems with unknown inputs are resolved necessary and sufficient conditions for the problem to have a solution the order of the minimal observer the properties of the closed loop system separation principle and general analytical expressions of the minimal order observer matrices all above results are first in the field

completions of noetherian p i rings abstract let r be a left noetherian p i ring and m a maximal semimaximal ideal in r satisfying i m i 0 it is proven that r z lim i r m i the completion of r with respect to m i is left noetherian settling affirmatively a conjecture of goldie g however usually r is neither left nor right flat over r and height m height m

some homological invariants of local pi algebras during the last several years artin jorgensen stafford yekutieli and others have generalized many homological results from the commutative case to the noncommutative connected graded case az sz1 jo1 jo2 ye in this paper we generalize some of those to the noncommutative local case our main interest is on noetherian local pi polynomial identity algebras though some results hold in a more general setting throughout a is an algebra over a base field k i is its jacobson radical and a0 a i if a0 is artinian a is called semilocal if a0 is a simple artinian algebra respectively a division algebra then a is called local respectively scalar local unless otherwise stated we are working with left modules and sometimes we use the term aop module for a right a module where aop is the opposite ring of a a finite a module means finitely generated over a we use noetherian respectively artinian for two sided noetherian respectively two sided artinian

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

noninteracting control of descriptor systems involving disturbances for m input p output descriptor systems involving disturbances it is proven that if the problem of disturbance rejection is solvable via static state feedback and the input output transfer function matrix is right invertible there always exists a static state feedback control law yielding simultaneously to disturbance rejection a triangular input output relation the structural properties of the closed loop system stability pole assignment etc are extensively studied

disturbance rejection of left invertible generalized state space systems a new approach is presented for the study of the disturbance rejection of left invertible generalized state space systems via pure proportional state feedback reducing the problem to that of solving a linear algebraic system of equations on the basis of this system of equations the necessary and sufficient conditions for the problem to have a solution are established in a form of simple algebraic criteria thus reducing the computational effort over known results and the general analytical expressions of the controller matrices are derived the structural properties of the closed loop system feedback invariant poles disturbance rejection with simultaneous elimination of the infinite poles are studied

the structure of robust disturbance rejection control this paper deals with the problem of disturbance rejection under state feedback in linear multivariable control systems this problem is ill posed under arbitrary state space parameter perturbations however it is shown that with respect to arbitrary perturbations of the plant transfer function coefficients a robust solvability condition and possibly a robust synthesis can be obtained these results are significant because the class of arbitrary state space parameter variations is too rich for practical interest whereas the class of arbitrary variations in transfer functions more closely represents the realistic problem of engineering concern

disturbance decoupling of linear time varying singular systems the problem of disturbance decoupling by state feedback is defined for a linear time varying singular system it is required that the closed loop system has a unique impulse free solution and its output is not affected by disturbances an algorithm namely disturbance decoupling algorithm is proposed it is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law based on the disturbance algorithm a constructive method is provided to design a disturbance decoupling feedback control law sufficient conditions for the solvability of the disturbance decoupling problem are derived it is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied