On representations for continuous dynamic systems

Through the use of a simple example involving a buffer tank, we illustrate the problems faced when attempting to formalize the dynamic aspects of a continuous process system. The problems are especially severe if we attempt to employ a purely qualitative representation. We show that the theoretical results obtained within qualitative reasoning describing the limits of qualitative simulation can be extended to cover the rule based approach as well. We conclude that for those cases where it is necessary to make predictions from a model of a dynamic system, we need a model based on a quantitative mathematical representation. Since representations of this type will not support any kind of reasoning about the system, apart from the computation of related values for variables, we need to employ some kind of hybrid approach to be able to make predictions about the evolution of variables while retaining the ability to reason about the behavior of the system at the same time.     

On the instability of large-scale systems

A set of sufficient conditions for the instability of large-scale systems is presented. These conditions are much less restrictive than similar conditions derived in [1].     

Minimal representations of MIMO time-varying systems and realization of cyclostationary models

This paper describes a family of minimally parameterized state-space models for completely n-step observable multi-input multi-output time-varying systems and their algebraical links with equivalent input-output models. These results are then used to develop an algorithm for the realization of generic input-output sequences generated by a periodic system. A complete numerical example is also developed to illustrate all steps of the algorithm described in the paper.     

On the realization of nonlinear discrete-time systems

It is shown, on the basis of a compact expression of the kernels of the discrete Volterra series associated to a linear analytic discrete-time system, that the kernels satisfy a suitable property which enables their inductive characterization. We also give a first result on the realization of a given family of functions by a linear analytic discrete-time system with linear invertible drift term.     

On doubly coprime fractional representations for lineartime-varying systems

Linear time-varying systems, which accept state-space realizations with continuous and bounded entries, form a noncommutative ring. The subset of this ring, which is comprised of L_p-stable systems, is a subring. Doubly coprime fractional representations for linear time-varying systems that belong to the subring of L_p-stable systems are constructed from the state-space realization of the system considered     

On formal power series representations for uncertain systems

The concept of minimality as developed for uncertain and multidimensional systems represented by linear fractional transformations (LFTs) is related to realization theory results for formal power series. We discuss the relationship between the notions of minimality for LFT and series realizations, and present a method for obtaining one type of minimal realization from the opposing type. An extension of an existing minimality result for formal power series to the multi-input-multi-output (MIMO) case is also presented     

On transfer function representations for homogeneous nonlinear systems

For stationary, homogeneous, nonlinear systems described via the Volterra functional representation, the Laplace transform of the system kernel is commonly used as a "transfer function." Corresponding to the symmetric and triangular forms of the kernel, special forms are obtained for the transfer function. We propose a new form for both the time-domain and transform-domain representation of homogeneous systerns. Properties of these so-called regular forms in relation to the other two forms and in regard to input/output computation, stability, and bilinear realization theory are discussed.     

On the well-posedness of large-scale interconnected systems

In this paper, we give a precise definition of well-posedness for a large-scale interconnected system, and derive several criteria for well-posedness. In the case of nonlinear systems, the criteria presented here are sufficient conditions for well-posedness, but they are graph-theoretic in nature and have a nice physical interpretation, both for continuous-time as well as discrete-time systems. In the case of linear time-invariant continuous-time systems, necessary and sufficient conditions for well-posedness are presented. Linear time-invariant discrete-time systems are not discussed here as they are adequately discussed elsewhere.     

On decentrally stabilizable large-scale systems

A class of large-scale systems is defined, which can always be stabilized by local feedback. Stability of the closed-loop system is connective and can tolerate nonlinearities in the interconnections. Any prescribed degree of stability can be achieved by an appropriate choice of the feedback gains.     

On a realization method for discrete-time linear systems

An algorithm to obtain the minimum state-space realization of a linear multivariable system, based on its parametric input-output model, is presented. A special canonic form for the state-space representation is used, which guarantees the uniqueness of the derived relationships between this representation and the input-output form.     

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems.     

On state representations of nonlinear implicit systems

The parameter identification problem in systems governed by partial differential equations is investigated. Stochastic approximation algorithms are applied for identifying a class of distributed systems driven by random inputs and observed through noisy measurements. No restrictions about the probability distributions are imposed. These algorithms converge with probability one, and are suitable for on-line applications. The proposed identification method assumes that a previous system classification has been performed, such that the model to be identified is known up to a set of space-varying parameters, where extraneous terms may be included. The very real case of noisy measurements taken at a limited number of discrete points Located in the spatial domain is considered.     

On the design of a decentralized observation scheme for large-scale systems

The problem of designing a decentralized observation scheme with a specified convergence rate for a large-scale system that may be described as an interconnection of several subsystems is considered. A new mathematical result for the factorization of the interconnection matrix in a certain form is given and its application to the observer design problem is discussed. The present results demonstrate how a knowledge of the existing interconnection pattern can be exploited for improving the efficiency in such designs.     

On the realization problem for stationary,homogeneous, discrete-time systems

For degree 2, stationary, homogeneous systems, we consider realizations in the form of state-affine difference equations, and in the form of feedback-free interconnections of stationary linear systems, adders, and multipliers. Realizability conditions are presented in terms of the symmetric transfer function (or kernel), and in terms of a new representation called the regular transfer function (or kernel). A procedure is given for constructing a minimal dimension state-affine realization, and the corresponding interconnection.     

On Hamiltonian realization of time-varying nonlinear systems

This paper investigates Hamiltonian realization of time-varying nonlinear (TVN) systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacopian matrix of a TVN system is nonsingu-lar, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is singular, this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non-singular main diagonal block. Furthermore, some sufficient (necessary and sufficient) conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.     

On flat systems behaviors and observable image representations

In this short paper we propose a definition of flatness for systems not necessarily given in input/state/output representation. A flat system is a system for which there exists a mapping such that the manifest system behavior is equal to the image of this mapping, and such that the latent variable appearing in this image representation can be written as a function of the manifest variable and its derivatives up to some order. For linear differential systems, flatness is equivalent to controllability. We will generalize the main theorem of Levine and Nguyen (Systems Control Lett. 48 (2003) 69) to general linear differential systems.     

On delay-independent stability of large-scale systems with timedelays

A new criterion for delay-independent stability of linear large scale time-delay systems is deduced by employing an improved Razumikhin-type theorem and the m-matrix properties. An illustrative example is given to demonstrate the superiority of the obtained results to those in the literature     

On stabilization of large-scale control systems using variable structure systems theory

A new approach to control design for large-scale systems using variable structure systems (VSS) theory is presented. Multilevel control concepts arc used to decompose a large control problem into a two-level algorithm such that each subsystem is stabilized with local discontinuous controllers and higher level corrective control is designed to take into account the effect of interactions among the subsystems. Two numerical examples are discussed as illustrations.