fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

characterization and optimization of l_ infty gains of linear switched systems in this paper we consider the l infty gain characterizations of linear switched systems lss and present various relevant results on their exact computation and optimization depending on the role of the switching sequence we study two broad cases first when the switching sequence attempts to maximize and second when it attempts to minimize the l infty gain the first named as worst case throughout the paper can be related to robustness of the system to uncontrolled switching the second relates to situations when the switching can be part to the overall decision making although in general the exact computation of l infty gains is difficult we provide specific classes the input output switching systems for which it is shown that linear programming can be used to obtain the worst case l infty gain this is a sufficiently rich class of systems as any stable lss can be approximated by one certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant lti compensation and further if the plant is strictly causal even a switched compensation which has a matched switching with the plant does not provide a better performance over an lti compensation also we present a new necessary and sufficient condition to check the stability of lss in form of a model matching problem on the other hand if one is interested in minimizing the l infty gain over the switching sequences we show that for finite impulse response fir switching systems the minimizing switching sequence can be chosen to be periodic for input only or output only switching an exact readily computable characterization of the minimal l infty gain is provided and it is shown that the minimizing switching sequence is constant which as also shown is not true for input output switching

on the stability of receding horizon lq control with zero state terminal constraint receding horizon control with zero state terminal constraint for linear time varying discrete systems is considered it is shown that uniform controllability suffices to ensure closed loop exponential stability thus relaxing the reversibility and or detectability requirements made in the existing literature the result has interesting implications in the design of predictive controllers with guaranteed closed loop stability

analysis of h 2 and h performance of discrete periodically time varying controllers abstract this paper presents analysis of the h 2 and h performance of discrete linear periodically time varying controllers for control of linear time invariant plants using a frequency domain lifting approach the analysis distinguishes periodically time varying control from time invariant control to show that the multiple transfer channels of the system time varying dynamics amplify the overall system gain such a result can provide deeper insights into the system time varying mechanism and clarify how the time varying dynamics acts and degrades the system performance quantitatively the paper presents necessary and sufficient conditions under which a linear time invariant controller can be found to provide strictly better control than periodically time varying controllers

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

stabilizing receding horizon h sub spl infin controls for linear continuous time varying systems in this note new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time varying systems under these conditions nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed it is proved that the proposed terminal inequality conditions ensure the closed loop stability of the receding horizon h sub spl infin control rhhc the stabilizing rhhc guarantees the h sub spl infin norm bound of the closed loop system the proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed loop stability include most well known existing terminal conditions as special cases the results for time invariant systems are obtained correspondingly from those in the time varying case

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

linear time varying h 2 optimal control of sampled data systems abstract the goal in this paper is twofold first it is shown that linear time varying control is in general superior to linear time invariant lti control for lti plants with an h 2 criterion an expression for the optimal performance using time varying control is derived and a condition under which there is no advantage in using linear time varying control over lti control is determined second the h 2 optimal control of continuous time systems is studied via dual rate sampled data controllers it is shown that such a problem can be recast via the lifting technique as a standard lti h 2 problem in discrete time a design procedure for the dual rate h 2 optimal controller is proposed

performance of periodically time varying controllers for sampled data control analyzes performance of periodically time varying sampled data controllers for l sub p deterministic and uniform disturbance rejection for a given linear periodic sampled data controller controlling a linear time invariant continuous time plant it is shown that a linear time invariant controller can be found to give better l sub p sampled data control than the time varying controller the performance analysis is in time domain using convexity properties of the l sub p signal space

h 2 performance of continuous time periodically time varying controllers abstract this paper uses a frequency domain approach to the analysis of h 2 performance of continuous time periodically time varying controllers for control of linear time invariant plants it is shown that the time varying dynamics of the periodic controller deteriorates the closed loop system h 2 performance and a linear time invariant controller can be found to provide strictly better h 2 control of the system

analysis of time varying control strategies for optimal disturbance rejection and robustness analysis of linear time invariant systems that are controlled by time varying controllers is given the problems of disturbance rejection and robustness are formulated and analyzed using functional analytic methods which reveal the properties that are common to these problems the theoretical development presented uses the theory and techniques of nuclear operators and their relation with the duality theory of tensor products of banach spaces the authors show how time varying compensation offers no advantage over time invariant compensation for the problem of disturbance rejection over general signal spaces in both continuous and discrete time and for the problem of l sub infinity robust stabilization of time invariant plants in addition another application of the theory for the problem of norm minimization subject to a norm constraint is presented

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

uniformly optimal control of linear time varying systems abstract an optimal control problem is formulated in the context of linear discrete time time varying systems the cost is the supremum over all exogenous inputs in a weighted ball of the sum of the weighted energies of the plant s input and output the controller is required to be causal and to achieve internal stability existence of an optical controller is proved and a formula for the minimum cost is derived

on the computation of the gap metric for ltv systems abstract in this paper we consider the robust stabilization problem for linear discrete time varying ltv systems using the gap metric in particular we show that the time varying tv directed gap reduces to an operator with a tv hankel plus toeplitz structure computation of the norm of such an operator can be carried out using an iterative scheme involving a tv hankel operator defined on a space of hilbert schmidt causal operators the infimization in the tv directed gap formula is shown to be in fact a minimum by using duality theory the latter holds as well in the time invariant case

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

lpv control of nonstationary systems a parameter dependent lyapunov approach the paper presents a parameter dependent lyapunov approach for the control of nonstationary linear parameter varying systems the work is motivated by the challenges encountered in controlling nonlinear systems about pre specified aggressive trajectories specifically ones which eventually settle into periodic orbits the control design method uses the l2 induced norm performance measure and the analysis and synthesis results are given in terms of parameterized linear matrix inequalities two fast and easy to implement algorithms for online controller construction are also provided

nonlinear time varying controllers for robust stabilization in this paper we consider the problem of robust stabilizallon for a certain class of plants with unstructured infinite dimensional uncertainty we demonstrate that for the problem of robustly stabilizing this class of plants linear time invariant controllers perform as well as nonlinear time varying nltv ones ihis in particular implies that adaptive control laws offer no advantage as far as the problem of robust stabilization of this class of plants is concerned as a corollary we demonstrate that the small gain theorem is both necessary and sufficient for a certain class of nltv operators

coprime fractional representations and stability of non linear feedback systems fractional representation methods for finite dimensional linear time invariant fdlti systems have been developed in an algebraic framework of principal ideal domains the concept of coprime fractional representations has been generalized to discrete time non linear systems by hammer 1985 1987 by viewing the bezout identity as the basis of the definition of coprimeness in this paper we view the role of right coprime fractional representation in representing the set of all stable input output pairs of a possibly unstable non linear system this notion of coprimeness is shown to be equivalent to that of fdlti systems using coprime fractional representations of non linear systems we obtain a characterization of the stability of non linear feedback systems this characterization is similar to that obtained in the case of fdlti systems we also obtain a parameterization of all non linear and time varying stabilizing controllers for linear possibly time varying plants which has the same form as t

a new approach for analysis and synthesis of time varying systems in this paper new techniques are developed for the analysis of linear time varying ltv systems these lead to a formally simple treatment of robust control problems for ltv systems allowing methods more usually restricted to time invariant systems to be employed in the time varying case as an illustration of this methodology the so called h sub spl infin synthesis problem is solved for ltv systems

on robust stability with structured time variant perturbations abstract we consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time invariant perturbations which are norm bounded the issue we address is the role that the type of perturbation norm plays in the robust stability conditions to this end the l p induced norm for 1 p on the perturbations is considered and it is shown that the structured singular value is the necessary and sufficient condition for robust stability for all these norms we conclude that for time invariant perturbations in contrast to the time varying case robust stability conditions are independent of the type of perturbation norms

robust controllers for uncertain linear multivariable systems abstract this paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems in the first part it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty in the second part in contrast with the first part it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known the type of plant uncertainty is the so called stable factor uncertainty and necessary and sufficient conditions are given for robust stabilization in the third part the model of uncertainty is a ball in the space of rational matrices metrized by the so called graph metric and sufficient conditions for robust stabilization are derived

periodic compensation of continuous time plants this note presents a periodic compensator which achieves robust stability for single input single output siso linear time invariant lti plants having both right half plane rhp poles and zeros a job lti controllers fail to do in addition for strictly proper plants this controller achieves model matching ensuring at the same time that the periodic oscillations present in the plant output are insignificant in magnitude the design steps are straightforward and linear algebraic in nature

parabolic problems in h 1 with fast growing nonlinearities tdepartamento de matem itica do icmsc universidade de sao paulo 13 560 silo carlos s p brazil and institute of mathematics silesian university 40 007 katowice poland also institute of mathematics of the polish academy of sciences received 18 march 1996 received f or publication 1997 key words and phrases parabolic equations fast growing nonlinearities global solutions dissipative semigroups global attractors 1 introduction

limitations of nonlinear discrete periodic control for disturbance attenuation and robust stabilization this paper presents a performance analysis of nonlinear periodically time varying discrete controllers acting upon a linear time invariant discrete plant time invariant controllers are distinguished from strictly periodically time varying controllers for a given nonlinear periodic controller a time invariant controller is constructed necessary and sufficient conditions are given under which the time invariant controller gives strictly better control performance than the time invariant controller from which it was obtained for the attenuation of l p exogenous disturbances and the robust stabilization of l p unstructured perturbations for all p 1

uniformly optimal control of linear time invariant plants nonlinear time varying controllers abstract it is shown that in the problems of uniformly or h optimal control of linear time invariant plants arbitrary nonlinear time varying controllers offer no advantage over linear time invariant controllers

global attractor for sectorial evolutionary equation an abstract differential equation with sectorial operator is shown to generate a dissipative semigroup whenever an appropriate introductory estimate for solutions is known based on hale s theory of dissipative systems such an a priori estimate is then shown to be sufficient for existence of a global attractor examples contained in the final part of the paper illustrate presented ideas 1996 academic press inc 1 introductory notes

performance robustness of discrete time systems with structured uncertainty given an interconnection of a nominal discrete time plant and a stabilizing controller together with structured norm bounded nonlinear time varying perturbations necessary and sufficient conditions for robust stability and performance of the system are provided it is shown that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem the resulting stability robustness problem is shown to be equivalent to a simple algebraic one the solution of which provides the desired necessary and sufficient conditions for performance stability robustness these conditions provide an effective tool for robustness analysis and can be applied to a large class of problems in particular it is shown that some known results can be obtained immediately as special cases of these conditions

stability of control systems and graphs of linear systems new conditions for internal stability of a closed loop control system are given in terms of the graphs of the multiplication operators induced by the transfer functions of the plant and the controller these conditions can be given a geometrical interpretation this relates closed loop stability to the minimal angle between the graph space associated with the system and the graph space associated with the controller the maximally stabilizing controller is defined as the controller that maximizes the minimum angle between the graph space associated with the system and the graph space associated with the controller it is shown that this controller can be calculated as a nehari extension of the coprime factors of the system

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

performance optimization of switched systems a model matching approach in this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time invariant lti systems the interest is placed on optimizing the worst case performance of this model matching system over all possible switchings with either l infin induced norm or h 2 norm as the performance criterion this optimization is performed over all youla kucera parameters that switch causally in time among n stable lti systems for the particular setup at hand it is shown that the optimal youla kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching and that it can be obtained as an lti solution to an associated standard l 1 or h 2 optimization in the case of matched switching two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin induced and h 2 norm optimizations an approximate solution with any given precision is possible by finite truncation applications of these results to sensitivity minimization linear switched parameter systems and cooperative control are provided

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

a convex optimization approach to signal reconstruction over switching networks in this paper we consider signal reconstruction over communication network channels that can be modeled as input switching systems such systems can be associated with a variety of applications including control and estimation over networks in particular we formulate the signal reconstruction problem as a prototypical model matching problem where the various mappings involved belong to a class of input switching systems the design interest is placed on minimizing the worst case or stochastic average performance of this model matching system over all possible switchings with an h 2 norm as the performance criterion this minimization is performed over all stable receivers r in the class of input switching systems for the particular setup at hand and in the case of matched switching two convergent sequences to the optimal solution from above and below respectively are formulated in terms of quadratic programs an approximate solution with any a priori given precision is possible by finite truncation also it is shown that in the cases of arbitrary partially matched or unmatched switching the optimal receiver r need not depend on the switching sequence and that it can be obtained as a linear time invariant solution to an associated h 2 norm optimization

robustness of discrete periodically time varying control under lti unstructured perturbations investigates robustness of linear periodically time varying lptv control of discrete linear time invariant lti plants subject to lti unstructured perturbations the note first derives a necessary and sufficient condition for robust stability of an lptv system subject to lti perturbations which is less conservative than the well known small gain condition it then presents a quantitative analysis on the robustness of lptv control under lti unstructured perturbations in comparison with that of lti control it is shown that under the normal value of the controller period suggested in the previous literature the stability margin is deteriorated by lptv control if lti unstructured perturbations are considered hence lti control is superior to lptv control in this respect

the gap metric robustness of stabilization of feedback systems in this paper we introduce the gap metric to study the robustness of the stability of feedback systems which may employ not necessarily stable open loop systems we elaborate on the computational aspects of the gap metric and provide upper bounds to the gap in cases where the exact formulas do not apply by admissible uncertainties we mean those which preserve closed loop stability and a specified small tolerance on the i o behavior of a feedback system we show that admissible uncertainties are precisely those which are constrained in the gap finally we conclude that any metric which preserves a continuous relationship between open loop systems and the corresponding stable feedback interconnections must have the topology of the gap metric

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

performance limitations of nonlinear periodic sampled data controllers for l sub p disturbance rejection this note presents a performance analysis of periodic nonlinear sampled data controllers for the rejection of l sub p specific and uniform disturbances earlier results on the performance of linear periodic controllers are extended to nonlinear controllers for a given periodic controller a time invariant controller is constructed which in general gives strictly better l sub p disturbance rejection performance than the periodic controller

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

squaring down and the problems of almost zeros for continuous time systems abstract in this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains we derive the minimal gain of the precompensator to achieve such a square system if the gain of this precompensator is too large then we derive an explicit trade off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system

structure and optimality of multivariable periodic controllers a linear periodic plant to be controlled by measurement feedback is considered the general optimal synthesis problem in which the objective is to select a compensator to minimize the norm of the induced map between the controlled output and the exogeneous input is analyzed it is shown that the performance of any linear compensator possibly time varying nonperiodic can be matched by a compensator contained in the restricted class of periodic controllers this result is established in the discrete time case for bounded amplitude l sub infinity signals in the continuous time case the result is shown for bounded energy signals l sub 2 l sub 2

on stability of constrained receding horizon control with finite terminal weighting matrix in this paper a new stabilizing receding horizon control based on a finite input and state horizon cost with a finite terminal weighting matrix is proposed for time varying discrete linear systems with constraints we propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints we show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality lmi in the case of constrained time invariant systems an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints using the invariant ellipsoid constraints a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

on lp disturbance rejection using periodic feedback control abstract in this paper the performance of discrete time periodically time varying controllers for rejection of l p specific and uniform disturbances is analyzed for control of linear time invariant plants this paper distinguishes linear time invariant controllers from linear non time invariant periodic controllers in the performance analysis for a given linear non time invariant periodic controller a linear time invariant controller is constructed and necessary and sufficient conditions are presented under which the linear time invariant controller gives strictly better l p control than the non time invariant periodic controller

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

time varying optimal disturbance minimization in presence of plant uncertainty the optimal robust disturbance rejection problem plays an important role in feedback control theory here its time varying version is solved explicitly in terms of duality and operator theory in particular the optimum is shown to satisfy a time varying allpass property moreover optimal performance is given in terms of the norm of a bilinear form the latter depends on a lower triangular projection and a multiplication operator defined on special versions of spaces of compact operators

finite time behavior of inner systems in this paper we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties for the class of linear time invariant dynamical systems these characteristics are determined by transmission zeros of the inner factor of the system transfer function the relation between nonminimum phase zeros and hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance the results are used to solve various tracking problems both on finite as well as on infinite time horizons a typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

monotonicity and stabilizability properties of solutions of the riccati difference equation propositions lemmas theorems fallacious conjectures and counterexamples abstract the problem considered is that of selecting an initial covariance matrix for the kalman filter to ensure that the closed loop filter at every subsequent time instant is exponentially asymptotically stable as a time invariant filter sufficient conditions are derived based on monotonicity properties of the solution of the riccati difference equation the results have application in observer design and the cases of filtering for nonstabilizable systems and systems with singular system matrices are included