on initial instantaneous jumps of singular systems this paper is concerned with instantaneous jumps in the state trajectory of a singular system it is shown that such jumps generically exist at the initial time due to inconsistent initial states the formula for the jumps is derived which indicates that the jumps linearly depend on the initial state moreover the set of all initial states which do not cause any state jumps for any output feedback is characterized and is revealed to be a linear subspace in the meantime the necessary and sufficient conditions are given for the existence of an output feedback to suppress completely the jumps for a given initial state finally we formulate the problem of designing an output feedback not only to stabilize the plant but also to achieve minimum initial jumps as a minimization problem

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

time varying discrete riccati equation in terms of ben artzi gohberg dichotomy abstract necessary and sufficient conditions for the existence of the stabilizing solution to the time varying discrete riccati equation are derived in terms of the so called ben artzi gohberg dichotomy it is shown that the problem of such existence conditions is strongly related to that of unique solvability in vector valued l2 spaces of a system of singular difference equations which in this case is termed the extended hamiltonian system ehs connections between the existence of the stabilizing solution to the riccati equation and the bounded invertibility of an appropriate l2 operator are pointed out via the notion of disconjugacy

two equivalent sets application to singular systems abstract in this paper we consider the problem of state feedback control design for continuous singular systems by applying equivalent sets technique a new formulation of dissipativity condition is proposed based on this condition the desired state feedback controller is designed such that the closed loop system is admissible and dissipative for singular markovian systems necessary and sufficient conditions are proposed for the system to be admissible and for the state feedback control design for time delay singular markovian systems a new bounded real lemma is proposed and the corresponding h control problem is studied numerical examples are given to illustrate the effectiveness of the theoretic results developed

stabilizing solutions of the h algebraic riccati equation the algebraic riccati equation studied in this paper is related to the suboptimal state feedback h control problem it is parametrized by the h norm bound we want to achieve the objective of this paper is to study the behavior of the solution to the riccati equation as a function of it turns out that a stabilizing solution exists for all but finitely many values of larger than some a priori determined bound on the other hand for values smaller than there does not exist a stabilizing solution the finite number of exception points can be characterized as switching points where eigenvalues of the stabilizing symmetric solution can switch from negative to positive with increasing after the final switching point the solution will be positive semidefinite we obtain the following interpretation the riccati equation has a stabilizing solution with k negative eigenvalues if and only if there exists a static feedback such that the closed loop transfer matrix has k unstable poles and an l norm strictly less than

stabilizability and positiveness of solutions of the jump linear quadratic problem and the coupled algebraic riccati equation this note addresses the jump linear quadratic problem of markov jump linear systems and the associated algebraic riccati equation necessary and sufficient conditions for stability of the optimal control and positiveness of riccati solutions are developed we show that the concept of weak detectability is not only a sufficient condition for the finiteness of cost functional to imply stability of the associated trajectory but also a necessary one this together with a characterization developed here for the kernel of the riccati solution allows us to show that the control solution stabilizes the system if and only if the system is weakly detectable and that the riccati solution is positive definite if and only if the system is weakly observable the connection between the algebraic riccati equation and the control problem is made as far as the minimal positive semidefinite solution for the algebraic riccati equation is identified with the optimal solution of the linear quadratic problem illustrative numerical examples and comparisons are included

h control for singular markovian jump systems with incomplete knowledge of transition probabilities this paper proposes a h state feedback control for singular markovian jump systems with incomplete knowledge of transition probabilities different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered moreover in contrast to the singular markovian jump systems studied recently the proposed method does not require any tuning parameters that arise when handling non convex terms related to the mode dependent lyapunov matrices and the corresponding self mode transition rates also this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism finally two numerical examples are provided to demonstrate the performance of h mode dependent control

class numbers of real cyclotomic fields of prime conductor the class numbers hl of the real cyclotomic fields q l l 1 are notoriously hard to compute indeed the number hl is not known for a single prime l 71 in this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields q l l 1 for the primes l 10 000 it is quite likely that these subgroups are in fact equal to the class groups themselves but there is at present no hope of proving this rigorously in the last section of the paper we argue on the basis of the cohen lenstra heuristics that the probability that our table is actually a table of class numbers hl is at least 98

time varying discrete riccati equation l sup 2 invertibility dichotomy and disconjugacy necessary and sufficient existence conditions for the stabilizing solution to the time varying discrete riccati equation are given the result is simply expressed in terms of the original input data via the l sup 2 uniformly bounded invertibility of an appropriate family of toeplitz like operators intimate connections with the notions of dichotomy and disconjugacy are also pointed out some aspects concerning the dependence of the existence conditions on the monotonicity of the input data are investigated as well

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

robust mathscr h _ infty control of t s fuzzy time delay systems via a new sliding mode control scheme this paper addresses the sliding mode control smc design problem for a class of uncertain nonlinear systems that can be represented by takagi sugeno t s fuzzy models we propose a novel dynamic sliding mode control scheme for t s fuzzy models aiming to eliminate the restrictive assumption that all subsystems share a common input matrix which is required in most existing fuzzy smc approaches sufficient conditions for the reachability of the sliding surface and asymptotic stability of the sliding motion are formulated in the form of linear matrix inequalities finally simulation results that illustrate the advantages and effectiveness of the proposed approaches are provided

on the non existence of certain classes of perfect p ary sequences and perfect almost p ary sequences we obtain new non existence results of perfect p ary sequences with period n called type p n the first case contains a class with type p equiv 5 pmod 8 p a qn the second case contains five types p equiv 3 pmod 4 p a q l n for certain p q and l moreover we also obtain similar non existence results of perfect almost p ary sequences

fast computation of achievable feedback performance in mixed sensitivity h design the computational bottleneck of the h infty design has been recognized to be the e iteration a computationally demanding direct search of the minimum achievable h infty performance verma and jonckheere showed that the optimal h infty performance can be characterized as the spectral radius of the so called toeplitz plus hankel operator even before the appearance of the toeplitz plus hankel operator in the h infty setting the same operator had already been shown to play a crucial role in the spectral theory of the linear quadratic problem developed by jonckheere and silverman in this paper we exploit this common toeplitz plus hankel operator structure shared by the seemingly unrelated linear quadratic and h infty problems and we construct fast state space algorithms for evaluating the spectral radius of the toeplitz plus hankel operator the salient feature of the algorithm is that the spectral radius can be evaluated with an accuracy predicted by an identifiable error bound from the antistabilizing solution of the algebraic riccati equation of the linear quadratic problem associated with the h infty design

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

analysis of continuous time kalman filtering under incorrect noise covariances abstract the behavior of the continuous time kalman filter under incorrect noise covariances is analyzed the filter performance is quantified by the actual state error covariance through this quantity the characteristic of the filter is examined convergence and divergence analyses of the actual state error covariance are given the significance of the results presented in the paper is that they help one to understand and be able to predict certain behavior of the kalman filter when inexact values of noise covariances are used

on the design of a stable adaptive filter for state estimation in high dimensional systems design of specific parametrized gain structures provides a new tool for ensuring stability of reduced order filter for high dimensional systems which is optimized adaptively in the minimum prediction error framework

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

inequality based properties of detectability and stabilizability of linear time varying systems in discrete time well known properties of uniform detectability and uniform stabilizability are sharpened in terms of lyapunov and riccati inequalities for discrete time linear time varying systems in particular it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite path of present and future coefficients these results are applied to time varying systems where the system coefficients vary among a finite set and lead to precise and computable convex conditions for the stability and dynamic output feedback stabilizability of such systems

data reduction in the mixed sensitivity h sup infinity design problem the mixed sensitivity h sup infinity design problem is discussed in the two block case the state space approach is used to investigate the internal structure of this design problem which inherits many pole zero cancellations the complete state space solution is provided efficient mathematical software can then be implemented

a spectral characterization of h optimal feedback performance and its efficient computation abstract we study the spectral properties of a toeplitz hankel operator which arises in the context of the mixed sensitivity h optimization problem and whose largest eigenvalue characterizes the optimal achievable performance 0 the existence of such an operator was first shown by verma and jonckheere 26 who also noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the iteration here we investigate this operator in detail with the objective of efficiency computing its spectrum we define an adjoint linear quadratic problem that involves the same toeplitz hankel operator as shown by jonckheere and silverman 13 16 consequently a finite polynomial algorithm allows 0 to be characterized as simply as the largest root of a polynomial finally a computationally more attractive state space algorithm emerges from the h t 8 lq relationship this algorithm yields a very good accuracy evaluation of the performance 0 by solving just one algebraic riccati equation thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e iteration

the class of suboptimal and optimal solutions to the discrete nehari problem characterization and computation simple and explicit formulae in a linear fractional transformation lft form for all suboptimal and optimal solutions to the discrete time version of the one block nehari problem are derived under no restrictive conditions imposed on the initial data using the so called signature condition a generalized popov theory type argument general solvability conditions in terms of a certain type of discrete time kalman szego popov yakubovich system are obtained for the class of optimal approximations derived via singular perturbation techniques the lft coefficients are all of mcmillan degree n r where n and r are the mcmillan degree and the multiplicity of the largest hankel singular value of the system to be approximated respectively the results also lead directly to a simple numerical algorithm

iterative residual generator for fault detection with linear time invariant state space models in this paper an iterative residual generator irg is proposed for discrete time invariant state space model with the aim of detecting faulty signals by minimizing the mean square errors subject to unbiasedness constraint a new filter with finite impulse response structure is derived the resulting irg is then obtained by extracting residual signal from the batch filter through several predictor corrector iterations it shows that irg can provide a zero mean gaussian process regardless of previous estimation errors more importantly it includes the residual generation process in the kalman filter as its special case with the chi square test a numerical example is simulated to demonstrate that irg can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults and the estimation horizon length in irg serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm

towards a link between the factorization approach and mimo robust adaptive control based on a doubly coprime factorization theorem nett et al 1984 an adaptive controller for discrete time mimo systems consisting of a not necessarily minimum phase modelled part and fraction type unmodelled dynamics which are not necessarily stable non linear and time varying is developed then by virtue of a stability result which is itself of interest it is shown that the adaptive closed loop system is bibo stable even in the presence of small but not necessarily stable unmodelled dynamics and arbitrarily bounded initial conditions consequently an initial but important step for applying the factorization approach to mimo robust adaptive control is completely established

nonfragile control with guaranteed cost of t s fuzzy singular systems based on parallel distributed compensation this paper investigates the nonfragile guaranteed cost control problem for a class of uncertain nonlinear singular state delayed systems that is described by takagi sugeno models the upper bound of state delay is assumed to be available a linear quadratic cost function is specified as the performance index of the closed loop system attention is focused on the fuzzy state feedback controller design via parallel distributed compensation scheme which not only guarantees the regular impulse free and asymptotically stable of the closed loop fuzzy singular delay system but also provides an optimized upper bound of the guaranteed cost function for the possibility of feedback gain variation and all admissible uncertainties all derived sufficient conditions are given in terms of linear matrix inequalities some numerical examples are provided to illustrate the effectiveness of the proposed design scheme

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

dynamic output feedback dissipative control for t s fuzzy systems with time varying input delay and output constraints this paper develops a new fuzzy dynamic output feedback control scheme for takagi sugeno t s fuzzy systems with time varying input delay and output constraints based on q s r alpha dissipativity the proposed controller called a q s r alpha dissipative output feedback fuzzy controller takes into consideration the abstract energy storage function and supply rate for the disturbance attenuation and provides a unified framework that can incorporate existing results for mathcal h infty and passivity controllers as special cases for t s fuzzy systems with time varying input delay and output constraints a dynamic parallel distributed compensator is used to design the q s r alpha dissipative output feedback fuzzy controller to ensure the asymptotic stability and strict q s r alpha dissipativity of closed loop systems described by a t s fuzzy model that satisfies some output constraints by employing the reciprocally convex approach a new set of delay dependent conditions for the desired controller is formulated in terms of the linear matrix inequality the effectiveness and the applicability of the proposed design techniques are validated by an example of control for active suspension systems for different road conditions

stability analysis of switched linear singular systems this paper addresses the stability analysis problem for switched linear continuous time singular systems first based on the equivalent dynamics decomposition form a refined description for state jumps of the switched singular system is presented which indicates that overall state jumps are resulted by two sequential state jumps second sufficient conditions for exponential stability of the switched singular system with stable subsystems are presented it is shown that the stability property of the system is completely determined by the switched reduced order dynamic subsystem and the switching law induced state jumps then a sufficient stability condition for the switched singular system with both stable and unstable subsystems is obtained finally numerical examples are presented to illustrate the effectiveness of the proposed approach

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

extended nehari problem for time variant discrete systems abstract in this paper a suboptimal solution to the time variant discrete version of the extended nehari problem is given the main tool used to obtain such a solution with prescribed tolerance is the so called anticausal stabilizing solution to the reverse discrete time riccati equation

optimal disturbance attenuation for discrete time switched and markovian jump linear systems an exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete time domain via the union of an increasing family of linear matrix inequality conditions associated with each markovian jump linear system is a switched linear system so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for markovian jump linear systems as well the results lead to semidefinite programming based controller synthesis techniques from which optimal finite path dependent linear dynamic output feedback controllers arise naturally in particular under the notion of path by path optimal disturbance attenuation finite path dependent controllers can outperform the usual mode dependent ones

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

stabilization of singular t s fuzzy markovian jump system with mode dependent derivative term coefficient via sliding mode control abstract this paper introduces sliding mode control for singular takagi sugeno t s fuzzy markovian jump system with mode dependent derivative term coefficient firstly a new continuous switching function is designed then sufficient conditions about admissibility of sliding motion under the case of completely known transition rate and uncertain transition rate are presented respectively the obtained conditions are strict linear matrix inequalities furthermore a sliding mode controller is presented finally an example is given to illustrate the effectiveness of the obtained results in this paper

brief paper optimal fault detection for linear discrete time varying systems this paper deals with the problem of observer based fault detection for linear discrete time varying ldtv systems a problem formulation is first proposed to address the optimization of the fault detection filter fdf design which is expressed in terms of maximizing a finite horizon h h or h h performance index this formulation can be applied to fdf design of ldtv systems subject to l 2 norm bounded unknown inputs or stochastic noise sequences it is shown that a unified optimal solution to the fdf can be obtained by solving the discrete time riccati equation and the optimal fdf is not unique a numerical example is given to illustrate the proposed method

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

anticausal stabilizing solution to discrete reverse time riccati equation abstract this paper is dealing with the problem of general conditions for the existence of the anticausal stabilizing solution to the discrete reverse time riccati equation the connection between the contracting property of the l2 input output operator of a linear internally stable system and the existence of the anticausal stabilizing solution to the above mentioned equation are pointed out

continuous and discrete time riccati theory a popov function approach abstract necessary and sufficient conditions for the existence of the stabilizing solution of the algebraic riccati equation are derived for both the continuous and the discrete time case under the weakest possible assumptions imposed on the initial data both frequency domain conditions involving an associated popov function and time domain conditions involving an associated matrix pencil are investigated

new results on output feedback h_ infty control for linear discrete time systems this note investigates the problem of output feedback h control for linear discrete time systems three types of h controllers are considered namely static output feedback controllers dynamic output feedback controllers and observer based output feedback controllers new design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality lmi representations which guarantee the prescribed h performances of the closed loop systems in contrast to the existing lmi conditions for designing the output feedback h controllers the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example

stabilizability of linear time varying systems abstract for linear time varying systems with bounded system matrices we discuss the problem of stabilizability by linear state feedback for example it is shown that complete controllability implies the existence of a feedback so that the closed loop system is asymptotically stable we also show that the system is completely controllable if and only if the lyapunov exponent is arbitrarily assignable by a suitable feedback for uniform exponential stabilizability and the assignability of the bohl exponent this property is known also dynamic feedback does not provide more freedom to address the stabilization problem the unifying tools for our results are two finite l 2 cost conditions the distinction of exponential and uniform exponential stabilizability is then a question of whether the finite cost condition is uniform in the initial time or not

admissibility analysis and control synthesis for t s fuzzy descriptor systems the problem of admissibility analysis and control synthesis for takagi sugeno fuzzy descriptor systems is investigated first based on nonquadratic fuzzy lyapunov function and fully using the information of fuzzy membership functions a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible regular impulse free and stable is proposed in which it is not necessary to require every fuzzy subsystem to be stable second the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions following the analysis both parallel and nonparallel distributed compensation controllers are designed linear matrix inequalities conditions are given to construct the controllers finally some examples are provided to illustrate the main results in this paper less conservative than some earlier related results

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

on sliding mode control of single input markovian jump systems in this paper an equivalent control based sliding mode control is proposed for single input linear markovian jump systems which guarantees the asymptotical stability furthermore by using the stochastic system theory a multi step state transition conditional probability function is introduced for the continuous markovian process which is used to define the reaching and sliding probabilities furthermore the formulas for calculating reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability extensive simulations are conducted to validate the theoretical results and show the relationship between the control force and reaching and sliding probabilities

on the evaluation of the least achievable tolerance in the disturbance feedforward problem abstract based on the so called generalized popov yakubovich theory the well known formula of the least achievable tolerance for the two block problem is easily recovered in a self contained way

on computing the spectral radius of the hankel plus toeplitz operator the square root of the spectral radius of the hankel plus toeplitz operator has been shown to be the achievable performance of the mixed sensitivity h sup infinity design the computation of the spectral radius is the bottleneck in the synthesis of the h sup infinity controller in this paper the spectral properties of the hankel plus toeplitz operator are investigated a finite procedure for computing the spectral radius of the hankel plus toeplitz operator is proposed

exponential asymptotic stability of time varying inverse prediction error filters it is a classical result of linear prediction theory that as long as the minimum prediction error variance is nonzero the transfer function of the optimum linear prediction error filter for a stationary process is minimum phase and therefore its inverse is exponentially stable here extensions of this result to the case of nonstationary processes are investigated in that context the filter becomes time varying and the concept of transfer function ceases to make sense nevertheless we prove that under mild condition on the input process the inverse system remains exponentially stable we also consider filters obtained in a deterministic framework and show that if the time varying coefficients of the predictor are computed by means of the recursive weighted least squares algorithm then its inverse remains exponentially stable under a similar set of conditions

stabilizing solution to the reverse discrete time riccati equation a matrix pencil based approach abstract we derive necessary and sufficient conditions for the existence of the stabilizing solution to the reverse discrete time riccati equation a particular type of algebraic riccati equation which is related to the solution of the discrete time version of the extended two block nehari problem the conditions are expressed in terms of the left stable deflating subspace of an associated symplectic matrix pencil in particular a maximum phase spectral factorization of the popov function is obtained under very relaxed conditions imposed on the initial data it is also proved that under a restrictive additional assumption the stabilizing solution to the reverse riccati equation reduces to the antistabilizing solution to the usual discrete time riccati equation a reliable numerical algorithm for computing the stabilizing solution to the reverse riccati equation is also presented together with formulae for the solution to the extended nehari problem

admissibility and stabilization of stochastic singular markovian jump systems with time delays abstract this paper deals with the admissibility analysis and stabilization of stochastic singular markovian jump systems ssmjss with time delays more general conditions for the existence and uniqueness of the impulse free solution to delayed ssmjss are presented consequently by constructing stochastic lyapunov krasovskii functional and applying generalized ito formula new sufficient conditions for the stability of ssmjss and delayed ssmjss are obtained in terms of strict linear matrix inequalities state feedback controller is designed to ensure stabilization of the delayed ssmjss three illustrative examples including an r l c circuit network and an oil catalytic cracking process are employed to verify the effectiveness and usefulness of the obtained results

composite fuzzy control of nonlinear singularly perturbed systems this paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed nsp systems with guaranteed hinfin control performance we use the takagi sugeno t s fuzzy model to construct the singularly perturbed fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained at first a set of common positive define matrices and the controller gains are determined by the lyapunov stability theorem and linear matrix inequality lmi approach then a sufficient condition is derived for the robust stabilization of nsp systems the composite fuzzy control will stabilize the original nsp systems for all epsivisin 0 epsiv and the allowable perturbation bound epsiv can be determined via some algebra inequalities a practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

sliding mode control in stochastic continuos time systems boldsymbol mu zone boldsymbol ms convergence it is shown that the sliding mode control smc technique can be successfully applied to stochastic systems governed by the stochastic differential equations of the ito type which contain additive stochastic unbounded white noise perturbations the existence of a strong solution to the corresponding stochastic differential inclusion is discussed to do this approach workable the gain control parameter is suggested to be done state dependent on norms of system states it is demonstrated that under such modification of the conventional smc we can guarantee the exponential convergence of the averaged squared norm of the sliding variable to zone around the sliding surface which is proportional to the diffusion parameter in the model description and inversely depending on the gain parameter k 0

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

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

spectral theory of the linear quadratic and h problems abstract an overview of the spectral theory of the linear quadratic and h problems is presented originally the spectral theory of the linear quadratic problem emerged out of the problem of characterizing the finite time escape of the riccati differential equation as a condition on the spectrum of a toeplitz plus hankel operator later and following an independent line of thought the spectral theory of the h problem emerged as a toeplitz plus hankel operator characterization of the smallest achievable tolerance in feedback design this common toeplitz plus hankel operator structure shared by the linear quadratic and h problems is elucidated by mapping the usual h frequency response specification into the time domain leading to an inequality bound on a quadratic functional precisely induced by the toeplitz plus hankel operator with this deep linear quadratic h connection at hand we derive a linear quadratic solution to the h problem and show that such issues as the adamjan arov krein problem pole zero cancellation in optimal h compensation etc can be fruitfully attacked using simple linear quadratic arguments

generalized continuous time riccati theory abstract a riccati like equation which incorporates as special cases the standard continuous time algebraic riccati equation and the constrained continuous time algebraic riccati equation is introduced and studied a characterization of the conditions under which an equation of general form has a stabilizing solution are investigated in terms of the so called proper deflating subspace of the extended hamiltonian pencil

class number computations of real abelian number fields in this paper we describe the calculation of the class numbers of most real abelian number fields of conductor 200 the technique is due to j m masley and makes use of discriminant bounds of a m odlyzko in several cases we have to assume the generalized riemann hypothesis introduction it is well known that the class number h of an abelian number field can be written as h h h where h is the class number of the maximal real subfield k of k and h is an integer we can determine the relative class number h in a straightforward way using the complex analytic class number formula see 7 kap iii or 9 chapter 3 section 3 for the full cyclotomic fields q n with 4o n 256 and their subfields one can deduce hfrom the tables of g schrutka von rechtenstamm 15 here dn denotes a primitive nth root of unity and 40 is the euler function for the class number factor h the complex analytic class number formula is less useful since it requires that the units of k be known alternative techniques have been developed by j m masley 13 who computed the class number of almost all real cyclic number fields of conductor 100 here the conductor of k is the least f for which k c q tf in this paper we apply masley s techniques with a few additions to determine the class numbers of a large collection of real abelian fields of conductor 200 see section 1 for a precise statement of our results some of which assume the generalized riemann hypothesis an important ingredient of masley s method is the use of discriminant lower bounds proved by a m odlyzko 14 these lead to an upper bound for the class number of a real abelian number field provided that its conductor or more precisely its root discriminant see 13 section 1 is sufficiently small it follows that this method can only be used for a finite number of real abelian number fields the existence of infinite class field towers shows that this remains true after any future improvement of odlyzko s bounds in fact examples of j martinet 12 show that the method will never apply to fields whose root discriminant is larger than five times the present bound under assumption of the generalized riemann hypothesis the structure of this paper is as follows section 1 contains our results and section 2 lists the theorems used in the proofs the proofs themselves are largely suppressed received october 24 1980 revised december 24 1981 1980 mathematics subject classification primary 12 04 12a35 12a55

simplified rapid switching gain scheduling for a class of lpv systems a limitation of the original gain scheduling approaches is that the closed loop stability can only be assured when the underlying parameters vary sufficiently slowly a remedy exists but requires for its implementation the possible solution of asymptotic riccati equations are for an infinite number of different parameter values and the on line solution of a riccati differential equation rde with time varying coefficient matrices our method avoids solving the rde online and instead uses an explicit transient formula that looks up the predetermined solutions of the associated ares at a finite set of given system operating points furthermore only a finite number of ares are solved to determine a finite set of controller gains

two riccati formulae for the discrete time h control problem a two riccati state space approach to the discrete time h control problem is presented the main theoretical tool is the kalman szego popov yakubovich system written in adequate forms in order to reduce the problems to a standard form for which the solutions are easily obtained the necessity part of our main results uses a signed counterpart of the positivity theorem

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

reverse discrete time riccati equation and extended nehari s problem abstract necessary and sufficient conditions for the existence of the anticausal stabilizing solution to the so called reverse discrete time riccati equation are derived under very relaxed conditions imposed on the initial data further a suboptimal solution of prescribed tolerance to the extended nehari s problem is constructed

time varying discrete riccati equation some monotonicity results abstract using a fre chet derivative based approach some monotonicity and comparison results concerning the solutions of the time varying discrete time riccati equation are obtained connections with the existence of the semistabilizing solution are made explicit as well

generalized discrete time popov yakubovich theory abstract this paper deals with the problem of general conditions for the existence of a stabilizing solution to the so called kalman szego popov yakubovich system the well known popov yakubovich positivity condition is replaced with a more general one expressed in terms of the invertibility of an adequate operator this allows one to consider also game theoretical situations

dissipativity based fuzzy integral sliding mode control of continuous time t s fuzzy systems this paper is concerned with dissipativity based fuzzy integral sliding mode control fismc of continuous time takagi sugeno t s fuzzy systems with matched unmatched uncertainties and external disturbance to better accommodate the characteristics of t s fuzzy models an appropriate integral type fuzzy switching surface is put forward by taking the state dependent input matrix into account which is the key contribution of the paper based on the utilization of lyapunov function and property of the transition matrix for unmatched uncertainties sufficient conditions are presented to guarantee the asymptotic stability of corresponding sliding mode dynamics with a strictly dissipative performance a fismc law is synthesized to drive system trajectories onto the fuzzy switching surface despite matched unmatched uncertainties and external disturbance a modified adaptive fismc law is further designed for adapting the unknown upper bound of matched uncertainty two practical examples are provided to illustrate the effectiveness and advantages of developed fismc scheme

sliding mode control of markovian jump systems with incomplete information on time varying delays and transition rates this paper is concerned with robust sliding mode control smc for continuous time markovian jump delay systems with incomplete transition rates trs the time varying delays are unclear and just bounded sometimes two methods are employed to investigate this control issue one is movement decomposition method by which reduced order sliding mode dynamics is obtained the other is via sliding mode observer and full order sliding mode dynamics is obtained on the estimation space in both cases sufficient conditions are established in terms of a set of coupled linear matrix inequalities lmis to ensure the sliding mode dynamics to be mean square exponentially stable moreover novel sliding mode controllers which need not full knowledge on time varying delays are synthesized to guarantee the reachability of the prescribed sliding surface finally numerical examples are provided to illustrate the effectiveness of the proposed methods

sliding mode control of singular stochastic markov jump systems an investigation has been made into the sliding mode control smc problem for singular stochastic markov systems ssmss in this paper by using replacement of matrix variables a new mean square admissibility criterion of ssmss is proposed first based on this admissibility criterion the desired state feedback controller is designed to guarantee the closed loop system to be mean square admissible then the obtained results given in the form of strict linear matrix inequalities are applied to solve smc problem of ssmss in order to illustrate the workability and applicability of the theoretic results developed numerical examples are provided

generalized discrete time riccati theory a riccati like equation termed the generalized discrete time algebraic riccati equation which incorporates as special cases both the standard and the constrained discrete time algebraic riccati equations is introduced and investigated under the weakest possible assumptions imposed on the initial data a complete characterization of the conditions under which such an equation of general form has a stabilizing solution is presented in terms of the so called proper deflating subspace of the extended hamiltonian pencil an evaluation of an associated quadratic index along constrained stable trajectories is given in terms of the stabilizing solution to the generalized riccati equation possible applications of the developed theory range from nonstandard spectral and inner outer factorizations to h 2 and h infty control in singular cases the results exposed in the present paper are the discrete time counterpart of those stated in the authors previous paper concerning the generalized singular continuous time riccati theory the results could be also seen as an extension to singular cases of the usual discrete time algebraic riccati equation theory of indefinite sign