quadratic stabilizability of uncertain linear systems existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control this note is concerned with the problem of stabilizing an uncertain linear system via state feedback control an uncertain system which admits a stabilizing state feedback control and some associated quadratic lyapunov function is said to be quadratically stabilizable in a number of recent papers conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control these papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result this note presents an example which shows that this implication is not true for more general uncertain linear systems to this end we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control

on the identification of certain rational transfer functions from truncated autocovariance sequences let h z spl sigma sub k 0 sup spl infin h sub k z sup k be a q spl times p rational causal minimum phase transfer function and let r sub n sub n spl isin z be the autocovariance sequence associated to the spectral density h z h sup t z sup 1 in this paper the authors address the identification problem of h z from the truncated autocovariance sequence r sub n sub n spl ne 0 for the case q p

optimization schemes for decomposition of fuzzy relations the paper proposes an optimization environment for decomposing fuzzy relations two basic categories of approaches are developed i based on direct gradient oriented optimization methods and ii exploiting the ideas of fuzzy neurocomputation these two approaches are carefully analyzed and contrasted making use of illustrative numerical material some immediate applications to pattern classification and fuzzy interpolation are studied in detail the study includes also some generalizations of the generic decomposition problem

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

on the robust stability of linear time invariant plants with unstructured uncertainty we consider general families of linear time invariant plants described by a nominal plant model with unstructured uncertainty we show under a rather weak assumption that when a family of systems is not robustly stabilizable by any linear time invariant feedback controller then no nonlinear time varying controller can robustly stabilize the given family

on optimal nonlinear feedback regulation of linear plants a design technique for optimal nonlinear regulation of linear plants based on a homogeneous feedback law of degree 2p 1 p frac 1 2 is developed

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

the optimal projection equations with petersen hollot bounds robust stability and performance via fixed order dynamic compensation for systems with structured real valued parameter uncertainty a feedback control design problem involving structured real valued plant parameter uncertainties is considered a quadratic lyapunov bound suggested by recent work of i r petersen and c v hollot 1986 is utilized in conjunction with the guaranteed cost approach of s s l chang and t k c peng 1972 to guarantee robust stability with robust performance bound necessary conditions that generalize the optimal projection equations for fixed order dynamic compensation are used to characterize the controller that minimizes the performance bound the design equations thus effectively serve as sufficient conditions for synthesizing dynamic output feedback controllers that provide robust stability and performance

on the convergence exponent of decomposable relations this paper deals with an decomposable fuzzy relation on 0 1 the decomposition problem of a fuzzy relation can be stated as follows given a fuzzy relation r determine whether there exist two fuzzy sets a and b such that r a b where the operator is nothing but godel implication at first two necessary and sufficient conditions that a fuzzy relation r is decomposable are given then the solution set of a and b with a b r is obtained in the end the convergence of the decomposable fuzzy relation is investigated and an algorithm is shown to calculate the convergence exponent for a given decomposable fuzzy relation

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

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

identification of rank one rational spectral densities from noisy observations a stochastic realization approach abstract let s be a q q spectral density matrix which is the sum of a rational rank one spectral density s 1 and of a constant positive definite matrix q the identification problem of s 1 and q from s is addressed the conditions under which s 1 and q are identifiable are first derived then an identification method is proposed it is based on a parametrization of the external stochastic realizations of s whose innovation sequence has a prescribed dimension

on the robust stabilizability of uncertain linear time invariant plants using nonlinear time varying controllers abstract we consider general families of linear time invariant plants described by a nominal plant model with additive or multiplicative unstructured modeling uncertainty we show that such families of plants are robustly uniformly stabilizable by nonlinear time varying controllers if and only if they are robustly stabilizable by linear time invariant ones some auxiliary results on hankel and l norm approximation are also obtained

on the identification of noisy ma models in this paper we address the identification problem of p input q output ma models corrupted by a white noise with an unknown covariance matrix in the case where p q under certain additional conditions we show that the generating function of the ma model is identifiable from the autocovariance function of the observation some simple algebraic identification procedures are also given

the general α decomposition problem of fuzzy relations abstract this paper deals with a general decomposition problem of fuzzy relations which can be stated as follows given a fuzzy relation r f x y determine two fuzzy relations q f x z and t f z y such that r q t where x resp y is a finite set firstly we point out that every fuzzy relation r is always generally decomposable and give an algorithm to construct q and t with r q t for a given r secondly we show that the general content r with r min z r q t q f x z t f z y is equal to the chromatic number of the simple graph f r generated by r therefore finding an exact algorithm for calculating r is an np complete problem

nonlinear versus linear control in the direct output feedback stabilization of linear systems this paper investigates the use of nonlinear direct output feedback in the control of linear time invariant systems inparticular it is concerned with those nonlinear controllers which result in a closed loop system which is quadratically stable that is the closed loop nonlinear system is asymptotically stable and furthermore a quadratic lyapunov function can be used to establish this stability the main result of this paper can be stated roughly as follows any linear system which can be made quadratically stable using nonlinear direct output feedback control can also be stabilized using linear direct output feedback control

the structure of decomposable indistinguishability operators decomposable fuzzy relations are studied symmetric fuzzy relations are proved to be generated by a single fuzzy subset for archimedean t norms decomposable indistinguishability operators generate special kinds of betweenness relations that characterize them a new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure is compatible with the betweenness relation generated by the relation is developed

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

decomposition and resolution of min implication fuzzy relation equations based on s implications the problem of solving min implication fuzzy relation equations based on s implications is studied in this paper decomposition of min implication fuzzy relation equations is given in a finite case the solution existence problem of min implication fuzzy relation equations is discussed and for ns implications a new solvability criterion based upon solution matrices introduced in this paper is studied it is shown that for each solution r of a min implication fuzzy relation equation there exists a maximal solution r of this equation such that r is greater than or equal to r whenever the solution set of this equation is nonempty the complete solution set of min implication fuzzy relation equation can be determined by the maximal solution set of this equation which is finite an effective method to solve min implication fuzzy relation equations based on s implication is proposed

extensions of mixed µ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory in this paper we make explicit connections between classical absolute stability theory and modern mixed analysis and synthesis specifically using the parameter dependent lyapunov function framework of haddad and bernstein and the frequency dependent off axis circle interpretation of how and hall we extend previous work on absolute stability theory for monotonic and odd monotonic nonlinearities to provide tight approximations for constant real parameter uncertainty an immediate application of this framework is the generalization and reformulation of mixed analysis and synthesis in terms of lyapunov functions and riccati equations this observation is exploited to provide robust reduced order controller synthesis while avoiding the standard d n k iteration and curve fitting procedures

parameter dependent lyapunov functions and the popov criterion in robust analysis and synthesis many practical applications of robust feedback control involve constant real parameter uncertainty whereas small gain or norm bounding techniques guarantee robust stability against complex frequency dependent uncertainty thus entailing undue conservatism since conventional lyapunov bounding techniques guarantee stability with respect to time varying perturbations they possess a similar drawback in this paper we develop a framework for parameter dependent lyapunov functions a less conservative refinement of fixed lyapunov functions an immediate application of this framework is a reinterpretation of the classical popov criterion as a parameter dependent lyapunov function this result is then used for robust controller synthesis with full order and reduced order controllers