Maria Anderlucci

An Unknown Input Observer for Singular Time-Delay Systems

The problem of state reconstruction is discussed for linear singular systems with a finite number of commensurable point delays using as models systems with coefficients in a ring. A geometric notion of conditioned invariant submodule is introduced for this class of systems over a ring and a design procedure is presented for constructing an observer in presence of unknown inputs

Efficient algorithms for geometric control of systems over rings

The computational algebra techniques described in this paper constitute a tool, efficient and easy to implement using the freely available software CoCoA. They open the way to an effective use of the geometric approach in dealing with dynamical systems over rings. Systems with coefficients in a ring can be used to model several interesting classes of dynamical systems such as parameter dependent systems or delay differential systems. The paper describes in detail, how the algorithms contained in the package “control.cpkg” can be used to practically solve decoupling problems for delay differential systems.

a residual generator for singular time-delay systems

The problem of residual generation is discussed for linear singular systems with a finite number of commensurable point delays using as models systems with coefficients in a ring. Using the geometric notion of conditioned invariant submodule, suitably defined for singular systems over a ring, a procedure is presented for constructing a residual generator for the fault detection and isolation for singular linear systems over a ring.

Disturbance decoupling problem for a class of descriptor systems with delay via systems over rings

In recent years, a considerable amount of research has been devoted to linear time-invariant descriptor systems (called also singular or differential–algebraic) and to delay differential systems because of their extensive applications. The presence of time delays, in fact, arises in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, etc. and may cause undesirable system transient response or even instability. Several results in literature are devoted to stability issues for descriptor systems with delays under the hypothesis that the considered system is ‘impulse free’, namely that the solution does not possess dynamical infinite modes nor impulsive behaviour (see, for instance, Liu & Xie, 1996; Fridman, 2002; Xu et al., 2002, 2005; Ma & Cheng, 2005). In this paper, under the same hypotheses, we will investigate the problem of finding a feedback law such that disturbances do not affect the output. The approach we follow here relies on the possibility of using mathematical models with coefficients in a suitable ring, or systems over a ring, for studying and analysing delay differential dynamical systems (see Conte & Perdon, 1982; Kamen, 1991 and references therein). The use of systems over rings is motivated by the fact that it avoids the necessity of dealing with infinite-dimensional vector spaces, like the state space of classical delay differential systems, and, in place, it allows the use of finite-dimensional modules. Although ring and module algebra is more rich and complicated than linear algebra, this makes possible to extend a number of techniques from the framework of linear dynamical systems, in particular the geometric approach. The geometric approach for the analysis and synthesis of linear systems with coefficients in a field (see Basile & Marro, 1969, 1992; Wonham, 1985) proved very effective in the solution of decoupling problems. The disturbance decoupling problem (DDP) for linear time-invariant singular systems (without delay) over a field was first formulated and solved by Fletcher & Aasaraai (1989) and, more recently, in Wang et al. (2004) by different methods. A geometric theory for dynamical systems over a ring,

Impulse elimination by derivative feedback for singular systems with delay

The impulse elimination problem by derivative feedback is investigated for linear singular systems with a finite number of commensurable point delays. Using as models linear singular systems with coefficients in a ring, an equivalent impulse elimination problem by derivative feedback is formulated for this class of systems and solvability conditions are provided. Several examples are worked out in details.

Disturbance Decoupling Problem for neutral systems with delay: A geometric approach

A geometric approach to the disturbance decoupling problem for linear neutral systems with a finite number of commensurable point delays is investigated and necessary and sufficient conditions for its solution are given. Using as models neutral linear systems with coefficients in a ring, new invariant submodules are defined together with algorithmic procedures for their computation. Examples are worked out in details.

GEOMETRIC DESIGN OF OBSERVERS FOR LINEAR TIME-DELAY SYSTEMS

Abstract The problem of designing an observer is considered for linear time delay systems with commensurable delays. The use of models over rings and of geometric methods allow us to develop a complete analysis of the problem and to describe constructive procedures for its solution.

Disturbance Decoupling problem for a class of Generalized State Linear Time-Delay Systems

Abstract The Disturbance Decoupling Problem by state feedback for linear generalized state systems with a finite number of commensurable point delays is formulated and investigated using as models linear singular systems with coefficients in a ring. Necessary and sufficient conditions for its solution are given in geometric terms, as well as algorithmic procedures to test them. Examples are worked out in details.

Disturbance decoupling problem for a class of descriptor systems with delay via systems over rings[republished article]

In recent years, a considerable amount of research has been devoted to linear time-invariant descriptor systems (called also singular or differential–algebraic) and to delay differential systems because of their extensive applications. The presence of time delays, in fact, arises in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, etc. and may cause undesirable system transient response or even instability. Several results in literature are devoted to stability issues for descriptor systems with delays under the hypothesis that the considered system is ‘impulse free’, namely that the solution does not possess dynamical infinite modes nor impulsive behaviour (see, for instance, Liu & Xie, 1996;Fridman,2002; Xu et al., 2002,2005;Ma & Cheng, 2005). In this paper, under the same hypotheses, we will investigate the problem of finding a feedback law such that disturbances do not affect the output. The approach we follow here relies on the possibility of using mathematical models with coefficients in a suitable ring, or systems over a ring, for studying and analysing delay differential dynamical systems (seeConte & Perdon , 1982;Kamen,1991and references therein). The use of systems over rings is motivated by the fact that it avoids the necessity of dealing with infinite-dimensional vector spaces, like the state space of classical delay differential systems, and, in place, it allows the use of finite-dimensional modules. Although ring and module algebra is more rich and complicated than linear algebra, this makes possible to extend a number of techniques from the framework of linear dynamical systems, in particular the geometric approach. The geometric approach for the analysis and synthesis of linear systems with coefficients in a field (seeBasile & Marro, 1969,1992;Wonham, 1985) proved very effective in the solution of decoupling problems. The disturbance decoupling problem (DDP) for linear time-invariant singular systems (without delay) over a field was first formulated and solved by Fletcher & Aasaraai (1989) and, more recently, in Wang et al. (2004) by different methods. A geometric theory for dynamical systems over a ring,

Observers and State Reconstructions for Linear Neutral Time-Delay Systems

Abstract The problem of state reconstruction is discussed for linear neutral systems with a finite number of commensurable point delays. Using as models systems with coefficients in a ring and following a geometric point of view, feasible and constructing procedures are proposed for the construction of observers of increasing complexity. Conditions are given to characterize neutral systems with delays for which linear observers exist not depending on the derivatives of the state. Some examples illustrating the results are worked out in details.