non iterative computation of infimum in discrete time h optimization and solvability conditions for the discrete time disturbance decoupling problem a non iterative method for the computation of the infimum for a class of discrete time h optimal control problems and the solvability conditions for the general discrete time disturbance decoupling problem are given in this paper the method for the computation of the infimum is applicable to systems where the transfer functions from the disturbance input to the measurement output and from the control input to the controlled output are free of unit circle invariant zeros and satisfy certain geometric conditions the solvability conditions we obtained for the general discrete time disturbance decoupling problem are also necessary and sufficient conditions

technical communique disturbance attenuation by dynamic output feedback for input delay systems this paper addresses the optimal disturbance attenuation problem by output feedback for multivariable linear systems with delayed inputs the attenuation is optimal in the sense that the controller minimizes the maximal amplitude of the plant output in response to such a disturbance the controller is a general feedback involving an observer a state predictor and a predicted state feedback the optimal disturbance attenuation problem is formulated in terms of an equivalent system without delay the optimal bound of the disturbance attenuation is then characterized and it is shown that the optimal controller tends to have high gains a necessary and sufficient condition to guarantee the existence of an optimal solution is provided using the geometric approach

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

when is a linear multi modal system disturbance decoupled in this paper we study the question under which conditions a linear multi modal system is disturbance decoupled we establish necessary and sufficient geometric conditions from which the existing results on switched linear systems and conewise linear systems can be recovered as special cases also we apply these conditions to a class of linear complementarity systems in order to obtain a more crisp characterization

system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

the h control problem with zeros on the boundary of the stability domain in this paper we study the discrete and continuous time h control problems without any assumptions on the system parameters our approach yields necessary and sufficient conditions for the existence of a suitable controller

almost stabilizability subspaces and high gain feedback the class of almost stabilizability subspaces is introduced as the state space analog of the class of stable but not necessarily proper transfer functions almost stabilizability subspaces can be considered as candidate closed loop eigenspaces associated with infinitely fast and stable modes we derive the basic properties of these subspaces and show that they can be approximated by regular stabilizability subspaces the relation with high gain feedback is elaborated upon in a number of applications

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

design for general h almost disturbance decoupling problem with measurement feedback and internal stability an eigenstructure assignment approach feedback controllers explicitly parameterized in a single parameter epsilon are constructed to solve the well known hinfinity almost disturbance decoupling problem with measurement feedback and with internal stability hinfinity addpms for continuous time linear systems the construction of these feedback laws utilizes eigenstructure assignment algorithms and does not involve the solution of any parameterized algebraic riccati equations as a result the coefficients of the feedback laws are explicitly given as polynomial matrices in epsilon the results generalize the earlier work of ozcetin et al by allowing the system to have invariant zeros on the imaginary axis such a generalization is motivated by the recent development of low gain feedback design technique

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

discrete time adaptive control of deterministic fast time varying systems in this note the earlier work of xie and evans on discrete time adaptive control for deterministic time varying systems is extended to the case of approximating the plant parameters by the truncated taylor series when the plant parameters are polynomials of time the algorithm will ensure that the closed loop system is globally convergent and globally stable it is shown that this scheme is able to control fast time varying plants more successfully than some previous schemes

brief paper on the geometric and dynamic structures of the h2 optimal and h central controllers in this paper the geometric structure of observer based controllers is investigated in order to characterize the controllable and unobservable subspaces of the h 2 optimal and the h central controllers it is shown that the controllable and unobservable subspaces of the h 2 optimal and the h central controllers can be characterized by the kernel and image subspaces of the solutions of two lyapunov equations under this characterization the connection between the geometric subspaces and the dynamic behavior of the plant and those of the h 2 optimal and h controllers is derived it is also shown that the h 2 optimal and the h central controllers inherit a certain part of the given plant dynamics in the geometric sense a numerical example is also given for illustration

reconfigurable control of piecewise affine systems with actuator and sensor faults stability and tracking a reconfigurable control approach for continuous time piecewise affine pwa systems subject to actuator and sensor faults is presented the approach extends the concept of virtual actuators and virtual sensors from linear to pwa systems on the basis of the fault hiding principle that provides the underlying conceptual idea the fault is hidden from the nominal controller and the fault effects are compensated sufficient linear matrix inequality lmi conditions for the existence of virtual actuators and virtual sensors are given that guarantee the recovery of closed loop stability and the tracking of constant reference inputs since lmis are efficiently solvable this solution leads to a tractable computational algorithm that solves the reconfiguration problem the approach is proven to be robust against model uncertainties and inaccurate fault diagnosis and is evaluated using an example system of interconnected tanks

the fixed poles of the disturbance decoupling problem and almost stability subspace mathcal v star_ b g rm ker c this paper is concerned with the fixed poles of the disturbance decoupling problem for linear time invariant systems by state feedback and measurement feedback algebraic characterizations for these fixed poles are given using the reducing subspace technique in numerical linear algebra these algebraic characterizations lead that the fixed poles can be directly computed by numerically reliable algorithms as an additional application of the reducing subspace technique we also develop a numerically stable method for computing the almost stability subspace mathcal v star b g rm ker c which is an extension of the method given by van dooren for computing the invariant subspaces in geometric control theory

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

semiglobal l sub 2 performance bounds for disturbance attenuation in nonlinear systems this paper addresses the problem of disturbance attenuation in the sense of l sub 2 gain with internal stability and no cost on the control input for nonlinear systems when the problem of almost disturbance decoupling is not solvable i e when the least achievable attenuation level between disturbance and regulated output is nonzero two different approaches are provided which facilitate the estimation of an upper bound for such a value

brief paper almost disturbance decoupling and pole placement we revisit here the almost disturbance decoupling problem addp willems 1981 by state feedback with the objective to solve addp and simultaneously place the maximal number of poles in the closed loop solution indeed when addp is solvable we show that whatever be the choice of a particular feedback solution the obtained closed loop system always has a set of fixed poles we characterize these fixed poles of addp the other non fixed poles can be placed freely and we characterize the optimal solutions in terms of ad hoc subspaces and feedbacks which allow us to solve addp with maximal pole placement from our contribution which treats the most general case for studying addp with maximal usually partial pole placement directly follow the solutions of addp with complete pole placement when there are no addp fixed poles and addp with internal stability when all the fixed poles of addp are stable without requiring the use of stabilizability subspaces as in willems 1981 we extend the concept of self bounded controlled invariant subspaces basile marro 1992 to almost ones an example is proposed that illustrates our contributions

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

almost disturbance decoupling with internal stability the almost disturbance decoupling problem with internal stability is solved in terms of the geometric concepts of linear systems theory the solution gives necessary and sufficient conditions for the existence of a dynamic output feedback controller such that in the closed loop system the disturbances are quenched say in the h sup infinity sense up to any degree of accuracy while maintaining a stable system matrix

almost invariant subspaces transmission and infinite zeros a lattice interpretation in the first part of the paper it is shown that the most important almost controlled invariant and almost conditionally invariant subspaces introduced by j c willems 4 5 are elements of the free distributive lattice generated by the well known subspaces download download full size image and download download full size image in the second part it is shown how the transmission zeros and the infinite zero structure may be obtained by duality within a state feedback context or an output injection one

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

transfer function conditions for output feedback disturbance rejection a recent paper 1 has derived state space conditions under which the disturbance transfer function in a linear multivariable system can be zeroed by a dynamic compensator forced by a prescribed set of measurements the present note derives necessary conditions for this problem in terms of the orders of the open loop control disturbance and measurement transfer functions these necessary conditions are shown to be generically sufficient for solvability moreover they provide additional insight into the geometric solvability conditions are simple to check and extend the corresponding results obtained for the state feedback case 2

almost disturbance decoupling with stabilization by measurement feedback abstract plants with two vector inputs and two vector outputs described by four rational transfer function matrices are considered necessary and sufficient conditions are given for the existence of a linear time invariant finite dimensional controller which when connected around one channel of the plant leads to an internally stable closed loop system such that the frequency response of the remaining channel becomes arbitrarily small as measured by the infinity norm

disturbance decoupling problems via dynamic output feedback this paper considers the disturbance decoupling problems with or without internal stability and pole placement via dynamic output feedback using polynomial and rational matrix techniques we show that in all three problems considered the central solvability condition can be expressed as a two sided matching problem a bxc where a b and c are the polynomial system matrices of certain natural subsystems of the system model and x is to be determined over various subrings of the rational functions this matching problem can in turn be reduced to certain appropriate zero cancellation conditions on the polynomial system matrices a b and c

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

full and reduced order observer based controller design for h_2 optimization in this paper the most general h2 control problem is considered we derive necessary and sufficient conditions when the infimum is attained by state feedback we do the same for the measurement feedback case where we derive necessary and sufficient conditions when the infimum is attained by proper dynamic compensators we also investigate reduced order compensators if some states are observable without noise we discuss for all of these cases the freedom that the non uniqueness of optimal compensators gives us in assigning the closed loop eigenvalues the second half of this paper investigates the case when the infimum cannot be attained we give a constructive algorithm to find a minimizing sequence of stabilizing controllers and discuss the freedom in the asymptotic locations of the closed loop eigenvalues again we do the above for three different cases static state feedback full order measurement feedback and reduced order measurement feedback

new structural invariants of linear multivariate systems abstract several sets e g lists of integers polynomials etc which remain invariant under a group of transformations including static output feedback control of a linear dynamic system are identified a nested feedback look decomposition of any given system is given which not only identifies the new invariants but also gives an algorithmic procedure of computing them as is known structural invariants such as the ones introduced here play important roles in many theoretical studies of control theory to show one such case here an upper bound to the minimum order of a dynamic output feedback compensator required to stabilize a given system is calculated in terms of the newly identified invariants this paper can be considered as an extension of the work of morse who identified structural invariants under static state feedback where as this paper identifies there are structural invariants under static output feedback

a determinantal proof of the craig sakamoto theorem abstract the craig sakamoto theorem states that if a and b are symmetric matrices then a i a b i a i b for all if and only if b ab 0 there are a number of proofs of this result the most common based on expansions of the logarithm of a the present proof is elementary in that it depends only on determinantal conditions

design for h almost disturbance decoupling problem with internal stability via state or measurement feedback singular perturbation approach an almost disturbance decoupling technique guaranteeing internal stability of a linear system while using either state feedback or only measurement feedback is considered under a set of necessary and sufficient conditions a state feedback controller is explicitly constructed similarly a full or reduced order observer based measurement feedback controller is explicitly constructed under a set of necessary and sufficient conditions all the developed controllers guarantee the asymptotic stability of the closed loop system in the absence of disturbances furthermore they can reduce h norm of the transfer function from the external disturbance to the controlled output to any arbitrarily specified value unlike other methods which merely give the solvability conditions our method explictly constructs them also our controllers are parametrized in terms of tuning parameters by the tuning of which the disturbance reflected in the output can be attenuated to any desired degree of accuracy