on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

l_ infty and l_ 2 low gain feedback their properties characterizations and applications in constrained control low gain feedback has found several applications in constrained control robust control and nonlinear control in this paper we first generalize the existing low gain design methods by introducing the notion of l vanishment and by providing a full characterization of feedback gains that achieve such a property we observe that l low gain feedback can lead to energy peaking namely the control energy required by l low gain feedback increases toward infinity as the low gain parameter decreases to zero motivated by this observation we consider the notion of l2 vanishment and establish several of its characterizations based on which a new design approach referred to as the l2 low gain feedback approach for linear systems is developed different from the l low gain feedback the l2 low gain feedback is instrumental in the control of systems with control energy constraints as an application of l2 low gain feedback the problem of semiglobal stabilization of linear systems with control energy constraints is solved in this paper the notions of l and l2 vanishment also allow us to establish a systematic approach to the design of l and l2 low gain feedback the advantage of this new design approach is that it results in a family of control laws including those resulting from the existing design methods

explicit solution to the singular discrete time stationary linear filtering problem a closed form solution to the stationary discrete time linear filtering problem is obtained explicitly in terms of the system state space matrices in the limiting singular case where the measurement noise tends to zero simple expressions in closed form are obtained for the kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the kalman filter closed loop matrix is derived the minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure and a remarkably different behavior of the solution in the minimum and nonminimum phase cases is found

the optimal projection equations for reduced order state estimation the singular measurement noise case the optimal projection equations for reduced order state estimation are generalized to allow for singular i e colored measurement noise the noisy and noise free measurements serve as inputs to dynamic and static estimators respectively the optimal solution is characterized by necessary conditions which involve a pair of oblique projections corresponding to reduced estimator order and singular measurement noise intensity

slow peaking and low gain designs for global stabilization of nonlinear systems this paper presents an analysis of the slow peaking phenomenon a pitfall of low gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems the phenomenon is best understood on a chain of integrators perturbed by a vector field up x u that satisfies p x 0 0 peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p x u these growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system when this higher order condition is satisfied an explicit control law is derived that achieves global asymptotic stability of x 0 this stabilization result is extended to more general cascade nonlinear systems in which the perturbation p x spl upsi spl upsi spl upsi spl xi u sup t contains the state spl xi and the control u of a stabilizable subsystem spl xi spl dot a spl xi u as an illustration a control law is derived that achieves global stabilization of the frictionless ball and beam model

explicit solutions to the singular discrete finite time linear estimation problem the problem of optimal filtering of linear discrete time processes is considered it is assumed that the driving and measurement noise signals are stationary white and that the number of measurements is finite explicit expressions for the filtering error covariance and the corresponding kalman gain matrices are obtained for the limiting case where the measurement noise intensity tends uniformly to zero similar expressions are derived for the limiting singular smoothing problem with finite number of measurements

loop transfer recovery techniques for discrete time optimal regulators using prediction estimators for discrete time lqg optimal regulators using current estimators it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum phase systems however current estimators cannot be used when the processing time of the controller is significant in this note the loop transfer recoveries using prediction estimators for square minimum phase systems are considered it is shown that although the perfect recoveries are impossible the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller

a generalized inverse solution to the discrete time singular riccati equation a closed form solution to the discrete time singular riccati equation is presented which is based on the moore penrose matrix inverse applications to deadbeat control and stabilizability are discussed

brief limiting performance of optimal linear discrete filters the limiting variance of the estimation error is obtained for the optimal h 2 filter for discrete time systems when the intensity of the measurement noise tends to zero in particular an explicit expression is obtained for the lowest achievable mean square error when the measurement noise is slowly varying and has intensity which tends to zero this limitation can be characterized completely by the system order the dimension of the process noise the number of the system s transmission zeros and the location of the system s unstable transmission zeros

stable hybrid adaptive control this paper examines the asymptotic properties of a hybrid adaptive control scheme while there are many different meanings of the word hybrid control in the literature we are referring to a scheme where the on line parameter estimation and underlying control design are carried out in a discrete time using digital electronics and do not require any analog multiplications or divisions this is of critical importance in practice since analog multipliers dividers are subject to serious drift and offset errors for such hybrid schemes we establish stability and an output tracking property without recourse to persistence of exitation the proof of stability requires a sufficiently fast sampling rate for the discrete time parameter estimation and the underlying control design

explicit solution to the singular lq regulation problem an explicit solution to the multivariable discrete linear quadratic lq regulation problem is obtained in the limiting singular case where the input weighting matrix tends to zero such a solution follows from a suitable spectral factorization of the input spectrum density matrix under the assumption that the system is stabilizable and detectable and that its transfer function matrix is of full rank the suitable spectral factor is shown to be the product of the system s minimum phase image and its unitary interactor matrix the unitary interactor matrix defined is a special case of the nilpotent interactor matrix defined by m w rogozinski et al 1987

the design of optimal reduced order stochastic observers for discrete time linear systems the minimum variance state estimation of linear discrete time systems with random white noise input and partially noisy measurements is investigated an observer of minimal order is found which attains the minimum variance estimation error the structure of this observer is shown to depend strongly on the geometry of the system this geometry dictates the length of the delays that are applied on the measurements in order to obtain the optimal estimate the transmission properties of the observer are investigated for systems that are left invertible and free of measurement noise an explicit expression is found for the transfer function matrix of this observer from which a simple solution to the linear discrete time singular optimal filtering problem is obtained

cheap optimal control of discrete single input single output systems this paper presents a solution to the linear discrete quadratic optimal control problem for a single input single output plant with a control weighting that tends to zero explicit expressions are derived for the optimal gain vector in terms of the first significant powers of the control weighting and the limiting values of these expressions are considered the optimal index of performance is obtained both for the minimum and non minimum phase plants the clear distinction between these two types of plants is discussed and the non vanishing value of the index of performance in the latter case is expressed in terms of the zero directions of the system extensions to the single input multi output case and the case where the index of performance is a function of dynamic operators are introduced

a closed form solution to the discrete time kalman filter and its applications abstract this paper presents a closed form solution to the discrete time kalman filter and its applications we first represent the kalman filter in terms of model parameters without using the riccati equation and requiring any artificial conditions such as invertibility of a system matrix and no system noises replacing the initial time with the fixed lag time to achieve the finite memory with respect to inputs and outputs and choosing the proper initial covariances on the recent finite horizon we easily obtain the minimum variance finite memory filter and then propose its iterative computation algorithm as another application a closed form solution to the difference riccati equation on the finite horizon is utilized to obtain a stabilizing gain matrix of a luenberger type filter as in ackermann s formula

sensitivity properties of a class of discrete time lqg controllers with computation delays sensitivity properties of the discrete time lqg controller which utilizes the optimal state predictor to compensate l step computation delays are discussed we obtain multiplicative decompositions of the sensitivity matrices at the input and output of a plant which clarify the effect of computation delays and imperfect observation furthermore these decompositions are used to show that duality between the sensitivity properties at the input and those at the output holds for l 1 and to identify the asymptotic sensitivity matrices obtained by loop transfer recovery procedures

robust detectability from the measurements plus state feedback stabilization imply semiglobal stabilization from the measurements we study the problem of stabilizing with large regions of attraction a general class of nonlinear system consisting of a linear nominal system plus uncertainties a similar result was given by the same author in previous works in this note we prove that what was referred in these works to as nonlinear coupling condition can be reformulated in the control design as a nonlinear rescaling of the lyapunov functions of the closed loop system plus the requirement for a suitably faster convergence of the state estimation error we obtain a paradigm very similar to the linear case for which if a couple of riccati like inequalities state feedback and observer design are satisfied then a measurement feedback stabilizing controller can be readily found examples are given for showing improvements over the existing literature

on prediction type reduced order observers for discrete time systems we define the combination of the standard reduced order observer with one step ahead state predictor as the prediction type reduced order observer we first obtain a simple and significant relation that ensures the equivalence of the reduced and the full order observers in the steady state we show the fact that a prediction type reduced order does not always provide a reduced order controller we also discuss the implications of the equivalence of the observers on state space representation of the doubly coprime factorization and yjb parametrization we use the equivalence relation to clarify the feedback properties achieved by the loop transfer recovery technique using the prediction type reduced order observer at both the input and output of a square and minimum phase plant in addition we discuss the computational requirements for the observer based controllers

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

singular filtering via spectral interactor matrix in this paper the notion of spectral interactor matrix sim for a given square transfer matrix is introduced and used in the singular filtering problem a sim is defined as an interactor matrix preserving the spectral properties of the underlying system after studying the class of all spectral interactor matrices associated with a given transfer matrix an algorithm for the computation of a sim is proposed by resorting to the sim it is possible to point out the role played by delays zeros at infinity and nonminimum phase zeros in the solution of the singular filtering problem

control under stochastic multiplicative uncertainties part ii optimal design for performance this paper studies the optimal control design problem for linear discrete time systems with stochastic multiplicative uncertainties these uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed i i d random processes the optimal performance under study is defined in the mean square sense referred to as the mean square optimal h 2 performance it is shown that the mean square optimal h 2 control problem via state feedback can be solved using a mean square stabilizing solution to a modified algebraic riccati equation mare a necessary and sufficient condition for the existence of this solution is presented which constitutes a generalization of the solution to the classic optimal h 2 state feedback design problem whereas the latter can be obtained by solving an algebraic riccati equation are it is also proven that the optimal control design problem can be cast as an eigenvalue problem evp for the output feedback case with possible input delays we show that the mean square optimal h 2 control problem also amounts to solving an mare when the plant has no nonminimum phase zeros from the inputs to the measurement outputs that is the global optimal solution is obtained by solving an mare incorporating the delays the implication is that in this case a separation principle still holds

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

semi global stabilizability of linear null controllable systems with input nonlinearities an h sub spl infin based lyapunov proof is provided for a result established by lin and saberi 1993 if a linear system is asymptotically null controllable with bounded controls then when subject to input saturation it is semi globally stabilizable by linear state feedback a new result is that if the system is also detectable then it is semi global stabilizable by completely linear output feedback further an extension which relaxes the requirements on the input characteristic is obtained

discrete time lqg ltr technique for systems with time delays loop transfer recovery ltr is applied for lqg controllers with prediction estimators for a class of square minimum phase discrete time linear systems with time delays we consider the class of plants described by the triple a b c whose time delay structure is characterized by the following hypothesis on the plant impulse response cb cab cad 2b 0 det cad 1b 0 when the estimator gain is fixed by recovery technique it is shown that the loop transfer matrix at the plant input is equal to the transfer matrix obtained with the optimal digital regulator having d sample controller delays described in 6 the dual result corresponding to the situation where the feedback gain is fixed by recovery technique is also analysed

modified least squares algorithm incorporating exponential resetting and forgetting in this paper we present the general analysis of a class of least squares algorithms with emphasis on their dynamic performance particularly in the presence of poor excitation the analysis is carried out in a deterministic framework and stresses geometrical interpretations the core of this paper is the proposal and analysis of a new algorithm which incorporates exponential forgetting and resetting to an unprejudiced treatment of data when excitation is poor the algorithm is particularly suitable for tracking time varying parameters and is similar in computational complexity to the standard recursive least squares algorithm the superior performance of the algorithm is verified via simulation studies

adaptive control for robot manipulators using discrete time identification an adaptive control scheme is proposed for rigid link robots where the control signal computations are performed continuously and the control coefficient computations are performed in discrete time a global boundedness result is established for the resulting scheme independent of the sampling rate it is also shown that the position velocity and acceleration tracking errors are of the order of the sampling period furthermore it is shown that if the reference trajectory is persistently exciting in a continuous time sense then for a sufficiently fast sampling rate the tracking errors decay to zero

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

dwell time controllers for stochastic systems with switching markov chain we study the problem of feedback stabilization of a family of nonlinear stochastic systems with switching mechanism modeled by a markov chain we introduce a novel notion of stability under switching which guarantees a given probability that the trajectories of the system hit some target set in finite time and remain thereinafter our main contribution is to prove that if the expectation of the time between two consecutive switching dwell time is sufficiently large then the system is stable under switching with guaranteed probability we illustrate this methodology by constructing measurement feedback controllers for a wide class of stochastic nonlinear systems

control of linear systems with measurement nonlinearities in this note we give a general result on the control of linear systems with measurement nonlinearities and multiple inputs and multiple outputs we prove that if the measurement nonlinearities satisfy a sector condition and the system has vector relative degree and its invariant zeroes have nonpositive real part then there exists a linear measurement feedback controller which semiglobally stabilizes the system

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

output feedback adaptive stabilization control design for non holonomic systems with strong non linear drifts this paper investigates the problem of output feedback adaptive stabilization control design for non holonomic chained systems with strong non linear drifts including modelled non linear dynamics unmodelled dynamics and those modelled but with unknown parameters an observer and an estimator are introduced for state and parameter estimates respectively by using the integrator backstepping approach and based on the observer and parameter estimator a constructive design procedure for output feedback adaptive stabilization control is given it is shown that under some conditions the control design ensures the closed loop system is globally asymptotically stable when there is no non linear drift in the first subsystem and semiglobally asymptotically stable otherwise an example is given to show the effectiveness of the theory

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

guaranteed stability margins for the discrete time linear quadratic optimal regulator the stability properties of the linear quadratic deterministic optimal regulator are investigated in the discrete time case guaranteed phase and gain margins are obtained for the regulator in terms of the singular values of the matrices of the regulator state space description these margins are compared to their continuous time counterparts and their implication on the regulator robustness is discussed

extended discrete time ltr synthesis of delayed control systems abstract this paper addresses compensation of dealys within a multi input multi output discrete time feedback loop for application to real time distributed control systems the delay compensation algorithm formulated in this paper is an extension of the standard loop transfer recovery ltr procedure from one step prediction to the general case of p step prediction p 1 it is shown that the steady state minimum variance filter gain is the h 2 minimization solution of the relative error between the target sensitivity matrix and the actual sensitivity matrix for p step prediction p 1 this concept forms the basis for synthesis of robust p step delay compensators p 1 the proposed control synthesis procedure for delay compensation is demonstrated via simulation of the flight control system of an advanced aircraft

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

decoupling properties of singular lq regulation problem some properties of a limiting solution derived from a standard lq regulator problem are discussed in the case where the input weighting matrix tends to zero for a discrete time system the explicit limiting solution is given in some literature it is shown that the limiting solution is closely connected with a disturbance decoupling problem moreover it is pointed out that the limiting feedback gain with the help of feedforward gain constructs the decoupled system with the maximum number of blocks

uniting local and global controllers for uncertain nonlinear systems beyond global inverse optimality abstract this paper provides a solution to a new problem of global robust control for uncertain nonlinear systems a new recursive design of stabilizing feedback control is proposed in which inverse optimality is achieved globally through the selection of generalized state dependent scaling the inverse optimal control law can always be designed such that its linearization is identical to linear optimal control i e h optimal control for the linearized system with respect to a prescribed quadratic cost functional like other backstepping methods this design is always successful for systems in strict feedback form the significance of the result stems from the fact that our controllers achieve desired level of global robustness which is prescribed a priori by uniting locally optimal robust control and global robust control with global inverse optimality one can obtain global control laws with reasonable robustness without solving hamilton jacobi equations directly

optimal nearly singular estimation of continuous linear stationary uniform rank systems the problem of optimal estimation of linear continuous systems is considered for the case where all the noise signals are stationary white and the intensity of the measurement noise tends uniformly to zero explicit expressions for the estimation procedures and the corresponding minimum error covariance matrices of the estimate are obtained in terms of the measurement noise intensity and the zero properties of the system these expressions are derived for the case where the first non zero markov parameter of the system is of full rank for the infinite and the finite time filtering problems they provide a simple geometric interpretation to the structure of the error covariance matrices and they distinctly show the difference between the estimation of minimum and non minimum phase systems the theory is developed both for square and non square systems

solution in the z domain to the discrete time stationary kalman filtering problem for systems with perfect measurements the discrete time stationary kalman filtering problem is solved in the z domain for general right invertible linear systems whose measurements are all noise free a simple expression in closed form is obtained for the transfer function of the optimal filter both for the uniform and the general nonuniform rank cases it provides an optimal solution also for systems with uniform and nonuniform time delays the minimum variance error of the estimate is analyzed and the independent contributions to this error of the system zeros outside the unit circle finite and infinite and the excess of the number of inputs over the number of measurements are investigated

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

from singular to nonsingular filtering of periodic systems filling the gap with the spectral interactor matrix with reference to periodic discrete time systems the concept of the periodic spectral interactor matrix operator psimo is introduced such an interactor enables one to transform the singular system into a nonsingular one with identical spectral properties this concept is useful to characterize the family of periodic solutions of the singular periodic riccati equation arising from the singular filtering problem the psimo is also a synthetic tool to represent the invariant zeros structure at infinity delays of periodic systems in an operational fashion

families of linear quadratic problems continuity properties in this paper we investigate for given one parameter families of linear time invariant finite dimensional systems the parameter dependence of the linear quadratic optimal cost optimal control inputs optimal state trajectories and optimal outputs it is shown that results that have been obtained in the past in the context of the problem of cheap control can in fact be generalized to a much broader class of parameter dependent cost functionals including cost functionals in which for every parameter value the weighting matrix of the control inputs is singular essentially only two assumptions on the parameter dependence of the cost functionals are required in order to have continuity of the optimal cost and optimal control inputs with respect to the underlying parameter one assumption is concerned with the continuity of the weighting matrices with respect to this parameter the other with the monotonicy of the weighting matrices with respect to the parameter instrumental in our development is a characterization of the linear quadratic optimal cost in terms of the so called dissipation inequality the results obtained are applied to the problem of cheap control and to a problem of priority control the latter provides an example of a family of quadratic cosl functionals with a polynomial parameter dependence

discrete time l and l2 norm vanishment and low gain feedback with their applications in constrained control the existing low gain feedback which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has been designed in very specific ways in this paper by recognizing the l and l 2 slow peaking phenomenon that exists in discrete time systems under low gain feedback more general notions of l and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals low gain feedback that does not lead to l and l 2 slow peaking in the control input are respectively referred to as l and l 2 low gain feedback based on the notions of l and l 2 vanishment not only can the existing low gain feedback be recognized as an l low gain feedback but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete time linear systems parallel to the effectiveness of l low gain feedback in magnitude constrained control the l 2 low gain feedback is instrumental in the control of discrete time systems with control energy constraints the notions of l and l 2 vanishment also result in a systematic approach to the design of l and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods

generalized dilations and the stabilization of uncertain systems via measurement feedback abstract we study the problem of semiglobally stabilizing uncertain nonlinear system z az bu p 1 z u t u y z p 2 z u t u with a b in brunowski form we prove that if p1 z u t u and p2 z u t u are of order greater than 1 and 0 respectively with generalized dilation l z u l1 nz1 l 1zn 1 zn lu and uniformly with respect to t where zi is the ith component of z then we can achieve semiglobal stabilization via arbitrarily bounded linear measurement feedback

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given