controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

pole assignment and observer design for continuous descriptor systems the problem of pole assignment and asymptotic observer design for multi input multi output continuous descriptor generalized state space systems is studied the problem is solved by introducing a new canonical form for controllable descriptor systems the internal stability of the descriptor variable feedback and observer configuration is also considered i e the extension of the separation principle to descriptor systems is given

design of a class of luenberger observers for descriptor systems a new approach to the design of a class of luenberger observers for descriptor systems is presented the design is performed in a straightforward manner the conditions required in the design are given in terms of the original system matrices the relationship among these and other well known conditions is highlighted

matrix pencil of closed loop descriptor systems infinite eigenvalue assignment abstract the regular matrix pencil se a bk is considered that characterizes a closed loop descriptor system u t kx t t a carefully contrived and efficient method is given for the determination of a set of matrices k such that the determinant se a bk is a constant value independent of s the problem is formulated as an infinite eigenvalue assignment by finite gain descriptor variable feedback via a singular value decomposition of the matrix e the result is interesting in its own right and finds application in controller and observer design

eigenstructure assignment for descriptor systems by output feedback compensation abstract a method for output feedback compensator design that assigns the eigenstructure of a descriptor system is presented the adopted approach is based on transforming the problem into that of eigenstructure assignment for a linear state space system using output feedback

observer design for descriptor systems two detectability notions are introduced for the most general class of linear descriptor systems necessary and sufficient conditions are derived for the detectabilities and for the existence of observers depending on existence conditions satisfied the observers can be either in the familiar luenberger form or in a generalized form i e in descriptor form as the original system itself is a unified procedure is provided for the design of observers in both forms

perfect observers for singular 2 d fornasini marchesini models a concept of the perfect observer for singular two dimensional 2 d fornasini marchesini models is proposed sufficient conditions are established for the existence of the perfect observer a procedure for design of the perfect observer is also derived and illustrated by a numerical example

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

robust stabilization of uncertain descriptor fractional order systems this paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional order systems with the fractional order a satisfying 0 a 2 the results are obtained in terms of linear matrix inequalities the parameter uncertainties are assumed to be time invariant and norm bounded appearing in the state matrix a necessary and sufficient condition for the normalization of uncertain descriptor fractional order systems is given via linear matrix inequality lmi formulation the state feedback control to robustly stabilize such uncertain descriptor fractional order systems with the fractional order a belonging to 0 a 2 is derived two numerical examples are given to demonstrate the applicability of the proposed approach

on the design of observers for generalized state space systems using singular value decomposition in this paper a method is developed for the design of luenberger type observers for linear time invariant control systems whose state equation is of the form ex ax bu where e is a singular square matrix the method is based on the singular value decomposition of the matrix e and on the reduction of the equation ex ax bu to a system consisting of a differential equation of the form w1 f1w1 f2 w2 g1u and an algebraic equation of the form h1w1 h2w2 g1u 0 if w2 can be eliminated from the differential equation by the aid of the algebraic equation and the original output equation of the system the method yields a reduced order observer for the generalized state space system

observers for descriptor systems for a singular non causal descriptor system of order n a p k lh order observer is proposed where p n q q is the number of infinite non dynamic modes of the system and k is the rank of a matrix obtained from a transformed system derived by using the singular value decomposition some useful results are given which establish the existence of this observer and which resolve problems encountered with pth order observers proposed in the literature robustness is achieved by choosing optimum gain matrices which reduce the sensitivity of observer performance to perturbations

observer design for discrete time descriptor systems an lmi approach abstract in this paper the observer design problem for discrete time descriptor systems is considered for the discrete time linear descriptor systems the necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved and a systemic design approach is presented via the linear matrix inequalities formulation furthermore an extension to a class of nonlinear descriptor systems with lipschitz constraints is investigated simulation examples are given to illustrate the estimation performance of the proposed method

design of observers for descriptor systems in this note simple and straightforward methods to design full and reduced order observers for linear time invariant descriptor systems are presented the approach for the reduced order observer design is based on the generalized sylvester equation sufficient conditions for the existence of the observers are given an illustrative example is included

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

observers for descriptor systems abstract the design of observers is investigated for the estimation of the descriptor vector x t of descriptor systems of the form ex t ax t bu t y t cx t such systems are divided into two categories non causal impulsive systems and causal impulse free systems for non causal systems an observer of order rank e is proposed and termed a full order observer since the dynamical order of a descriptor system is regarded as rank e for causal systems it is shown that the number of independent outputs m does not exceed rank e and an observer of order rank e m is introduced and termed a minimal order observer the approach is based on the transformation of the system into particular design coordinates via a singular value decomposition of the matrix e illustrative examples are included

adaptive observer for continuous descriptor systems we design an adaptive observer for a stable single input and single output continuous descriptor generalized state space or singular system under the assumption that the descriptor system is observable it is transformed into what we call descriptor observer canonical form this form also allows the descriptor variable to be represented by a linear combination of the 2n unknown parameters and the filtered input and output measurement we also show that the estimates converge to the true values when the bounded input satisfies the richness condition under the assumption that the system is controllable

a new algorithm for an eigenvalue assignment problem from singular control theory in this paper a new numerical algorithm for an eigenvalue assignment problem which arises from a singular system control is developed the algorithm is based on orthogonal row column compressions which can be implemented in a numerically reliable way

eigenvalue placement for generalized linear systems this paper deals with some aspects of eigenvalue placement by state feedback for generalized linear systems described by e ax bu where e is a singular map it is shown that controllability of the infinite eigenvalues of the pencil se a is equivalent to the existence of a state feedback map which assigns those eigenvalues to pre specified complex numbers a procedure for the assignment of all eigenvalues to distinct complex numbers is also discussed

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

output feedback of forward backward periodic systems stability an n periodic forward backward system defined by a collection of nonproper rational matrices is considered in addition an n periodic collection of output feedbacks such that the closed loop system is n periodic and forward backward is constructed block ordered coprime factorizations of a rational matrix are used in the stabilization of that closed loop system

observers for singular systems the following three major aspects of the design of observers for linear time invariant singular systems are resolved the necessary and sufficient conditions for the problem to have a solution the order of the minimal observer and the properties of the closed loop system separation principle an algorithm is presented for the construction of the minimal order observer

descriptor systems decomposition into forward and backward subsystems it is shown that a decomposition of the descriptor space with certain properties induces a decomposition of the descriptor system into forward and backward subsystems different decompositions correspond to different apportionments of the required boundary conditions between initial and final times applications include several different but equivalent methods for solving the descriptor system and a clarification of the relations between some previously known methods of solution

regularity and stability analysis of discrete time markov jump linear singular systems abstract in this paper the regularity and stability analysis of discrete time markov jump linear singular systems mjlss is performed when dealing with singular systems a primary concern is related to the existence and uniqueness of a solution to the system this problem that is called regularity problem has a known solution when the linear singular system is not subject to jumps lss it turns out that when the pair of matrices that describes the dynamics of the lss satisfies a certain condition then it is regular by extending this condition to mjlss a unique solution for this class of systems is derived indeed through the idea of mode to mode regularity which is stronger than the mode by mode notion that can be found in the literature the existence of a unique solution of an mjlss is shown furthermore for systems that are mode to mode regular it is shown how to obtain recursive second moment models whose complexity depends on how anticipative the systems is the derived results on regularity and second moment modeling enable us to study stability of an mjlss by following the literature on markov jump linear systems mjls four different concepts of stability are introduced and their relationship is established the results presented in this paper generalize well known results concerning the stability given in the mjls theory for instance it is shown that the stability of the system is equivalent to the spectral radius of an augmented matrix being less than one as happens in the theory of mjls

observer design for generalized state space systems with unknown inputs abstract the following four major aspects for the observer design problem for generalized state space systems with unknown inputs are resolved necessary and sufficient conditions for the problem to have a solution the order of the minimal observer the properties of the closed loop system separation principle and general analytical expressions of the minimal order observer matrices all above results are first in the field

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

comments on on the robust popov criterion for interval lur e systems this paper supplements the remarks made in a paper by dahleh et al ieee trans automat contr vol 38 p 1400 5 1993 regarding the popov sector of lur e systems with interval plants a numerical example is provided to show that strict inequalities hold among three sectors those obtained by the theorem of the paper by applying popov theorem to each member system and by applying that to each of the systems with kharitonov plants this counterexample negates a tempting conjecture on strong robust popov criterion

a simple procedure for the stabilization of a class of uncontrollable generalized systems this paper gives a simple procedure for the stabilization with a prescribed rate of convergence of the free motions of a class of possibly single input uncontrollable generalized continuous time time invariant linear systems preserving the impulse free property if any