representations of kac moody and virasoro algebras on modules of greenberg mohapatra algebras the theory of greenberg mohapatra algebras is developed in continuation to a previous paper standard cyclic modules are constructed for the algebras and on them kac moody and virasoro algebras are represented through a basic procedure the representations of kac moody and virasoro algebras help to understand the structure of greenberg mohapatra algebras and the question of possible violation of the pauli exclusion principle

fault detection and isolation for unstable linear systems in the design of a residual generator for an unstable plant the unstable modes are made unobservable from the residual vector we point out that this cannot be achieved in practice due to the discrepancy between the estimated model and the true plant model hence we deduce that it is not possible to design a residual generator for an unstable plant unless it is stabilized by an adequate controller as a by product we provide expressions which can be used to quantify the effect of modeling uncertainties on the performance of a residual generator the factorization approach to control theory is used for the developments

observability quadratic normal form for discrete time systems this note deals with quadratic observability normal form for nonlinear discrete time single input single output siso system first of all the main concept of quadratic equivalence with respect to the observability property is introduced for discrete time systems subsequently normal form structure for discrete time system is developed for system with unobservable linear approximation in one direction finally the effect of the so called resonant terms on the observer design and synchronization of chaotic systems is pointed out in an illustrative example

nonlinear control via uniform system approximation abstract we introduce the notion of uniform system approximation and use it to solve the following problem given a single input nonlinear system f g x f x g x u that is linearly controllable on a manifold e of equilibrium points find vector fields f g such that f g and f g agree to first order on e and f g is input to state linearizable on a neighborhood of e the solution proceeds by constructing a linearizable uniform system approximation and yields as a by product a feedback control law that can be used to guarantee stable operation of the given system in a neighborhood of e this includes for example smooth transitions between operating points that are not necessarily close to each other a simple example is given to illustrate the approach

normal forms and approximated feedback linearization in discrete time abstract the paper discusses approximated feedback linearization of nonlinear discrete time dynamics which are controllable in first approximation and introduces two types of normal forms the study is set in the context of differential difference representations of discrete time dynamics proposed in monaco normand cyrot in normand cyrot ed perspectives in control a tribute to ioan dore landau springer londres 1998 pp 191 205

nonlinear discrete time control of systems with a naimark sacker bifurcation in this paper we study the problem of the stabilization of nonlinear control system with one complex uncontrollable mode we find normal forms and quadratic invariants then we compute center manifolds and use bifurcation theory to synthesize quadratic controllers

approximate linearization by state feedback and coordinate change a nonlinear system can always be approximated to first order by linear systems it has been shown by jakubczyk and respondek 4 and hunt and su 3 that certain nonlinear systems are the exact transforms of linear systems under nonlinear state coordinate change and nonlinear state feedback in this paper we give necessary and sufficient conditions for a nonlinear system to be approximated to higher order by the transform of a linear system the use of this technique in the design of nonlinear compensators has been suggested recently by the author 6

detection filter design spectral theory and algorithms a new formulation of the detection filter problem is generated by assignment of the closed loop eigenstructure under certain constraints detection filters which are actually a specific class of observers fix the output error direction of the system so that it can be associated with a particular failure mode and its known design failure direction the derivation of detection filters from an eigensystem assignment approach permits a very transparent theory the detection filter gains and closed loop eigenvectors are obtained from a set of simultaneous equations necessary and sufficient conditions for the solution of these algebraic equations are determined which produce a complete theory for detection filters

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

discrete time transitivity and accessibility analytic systems a basic open question for discrete time nonlinear systems is that of determining when in analogy with the classical continuous time positive form of chow s lemma accessibility follows from transitivity of a natural group action this paper studies the problem and establishes the desired implication for analytic systems in several cases i compact state space ii under a poisson stability condition and iii in a generic sense in addition the paper studies accessibility properties of the controllability sets recently introduced in the context of dynamical systems studies finally various examples and counterexamples are provided relating the various lie algebras introduced in past work

observer based fault detection and isolation filter design for linear time invariant systems in this paper we consider a model based fault detection and isolation problem for linear time invariant dynamic systems subject to faults and disturbances we use a state observer scheme that cancels the system dynamics and defines a residual vector signal that is sensitive only to faults and disturbances we then design a stable fault detection and isolation filter such that the norm of the transfer matrix function from disturbances to the residual is minimised for fault detection subject to the constraint that the transfer matrix function from faults to residual is equal to a pre assigned diagonal transfer matrix for isolation of possibly simultaneous occurring faults our solution is given in the form of linear matrix inequalities using state space techniques as well as a model matching problem using matrix factorisation techniques a numerical example is given to illustrate the efficiency of the fault detection and isolation filter

two constructions of affine lie algebra representations and boson fermion correspondence in quantum field theory we establish an isomorphism between the vertex and spinor representations of affine lie algebras for types dl 1 and dl 1 2 we also study decomposition of spinor representations using the infinite family of casimir operators and prove that they are either irreducible or have two irreducible components we show that the vertex and spinor constructions of the representations can be reformulated in the language of two dimensional quantum field theory in this physical context the two constructions yield the generalized sine gordon and thirring models respectively already in renormalized form the isomorphism of representations implies an equivalence of these two models which is known in quantum field theory as the boson fermion correspondence

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction

reliable control using redundant controllers this paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant the resulting closed loop control system is reliable in the sense that it provides guaranteed internal stability and h sub spl infin performance in terms of disturbance attenuation not only when all controllers are operational but also when some controller outages sensor and or actuator occur a numerical example is given to illustrate the proposed design procedures

extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems in this paper a set of extended quadratic controller normal forms of linearly controllable nonlinear systems is given which is the generalization of the brunovsky form of linear systems a set of invariants under the quadratic changes of coordinates and feedbacks is found it is then proved that any linearly controllable nonlinear system is linearizable to second degree by a dynamic state feedback

the algebras of inhibited parafermionic violation of the pauli principle the theory of the algebras of ignat ev and kuz min and of greenberg and mohapatra is developed these are algebras of inhibited parafermionic oscillators that describe possible small violations of the pauli exclusion principle the cyclic modules of the algebras are constructed so as to exhibit the connection of their fundamental properties as uniqueness and statistical signature with the relations in the algebras the formalism is presented in such a way suited for further mathematical and physical developments and has a natural continuation in a forthcoming paper

approximate and local linearizability of nonlinear discrete time systems we consider a single input non linear discrete time system of the form where x n u and f x u n 1 n is a c n valued function necessary and sufficient conditions for approximate linearizability are given for we also give necessary and sufficient conditions for local linearizability finally we present analogous results for multi input non linear discrete time systems

fault detection via factorization approach abstract problems of designing fault detection and identification filters in the frequency domain are formulated and solved using the factorization approach a characterization of all fault detection filters is derived this enables the derivation of necessary and sufficient conditions for the existence of fault identification as well as detection and isolation filters it is shown that these conditions are a generalization of existing results the formulas of constructing the filters are also derived in comparison with the algorithms given in previous work they are computationally straightforward and simple finally the proposed method for designing fault identification filters is extended so that more practical cases can be handled

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature