1,721,303 research outputs found
On the control of finite support behaviors
No full textIn the paper the main properties of finite support behaviors are introduced and characterized in terms of the polynomial matrices involved in their representation. Necessary and sufficient conditions for the existence of an input/output (possibly, non-anticipating) description of a finite support behavior are given.
The control problem is also addressed, and properly restated in the behavior theory context as an interconnection problem. Conditions for the existence of controllers that make the resulting connected system observable, as well as a complete description of the class of characteristic polynomials that the resulting controlled system possibly exhibits, are given. Finally, the problem of controlling a dynamical system in input/output from by means of a controller with the same structure, is investigated and solved
Driving variable realizations and the nonnegative realization problem for controllable behaviors
No full textNon-negative linear systems, traditionally investigated within the state-space framework,
have been recently analysed within the behavioural setting. In a couple of recent papers
[J. W. Nieuwenhuis, ‘‘When to call a linear system nonnegative’’, Linear Algebra & its
Appl., 281, 1998, pp. 43–58.; M. E. Valcher, ‘‘Nonnegative linear systems in the behavioural
approach: the autonomous case’’, Linear Algebra and its Appl., 2000, 319, pp. 147–162.],
several definitions and results about non-negative behaviours (and, in particular, about
non-negative autonomous behaviours) have been derived. Moreover, the non-negative
realization problem for autonomous behaviours has been fully explored in [M. E. Valcher,
‘‘Non-negative realization of autonomous systems in the behavioral approach’’, SIAM J. on
Control and Opt., 2001, 40, pp. 540–556.], thus deriving an extended set of necessary and
sufficient conditions for an autonomous behaviour to admit a non-negative realization.
Here, we focus our attention on the non-negative realization problem for controllable
behaviours. To this end, we first address the general realization problem by means of a driving
variable (DV) state-space representation, and investigate under what conditions a state-space
model provides a DV realization of a controllable behaviour. Based on these results, we
analyse the possibility of realizing a controllable behaviour by means of a non-negative DV
representation and, in particular, a reachable non-negative DV realization. Moreover,
necessary and sufficient conditions for a behaviour to be the controllable part of a (complete)
behaviour endowed with a non-negative realization are presented
Controllability and reachability criteria for discrete time positive systems
No full textDiscrete time positive systems have been the object of widespread interest in the literature. In the last decade particular attention has been devoted to the analysis and characterization of the different notions of reachability and controllability which, in this context, make their appearance. In this paper, the properties of (ordinary and essential) controllability and reachability are analysed. Based on a graph-theoretic approach, we provide practical criteria to verify whether a given positive system (F, G) is endowed with these properties, together with canonical forms for describing reachable/controllable pairs
On the internal stability and asymptotic behavior of 2-D positive systems
No full textTwo-dimensional (2-D) positive systems are 2-D state-space models whose variables take only nonnegative values and, hence, are described by a family of nonnegative matrices. The free state evolution of these systems is completely determined by the set of initial conditions and by the pair of nonnegative matrices, (A.B), that represent the shift operators along the coordinate axes. In this paper, internal stability of 2-D positive systems is analyzed and related to the spectral properties of the matrix sum A+B. Also, some aspects of the asymptotic behavior are considered, and conditions guaranteeing that all local states on the same separation set Ct assume the same direction as t goes to infinity, are provided. Finally, some results on the free evolution of positive systems corresponding to homogeneous distributions of the initial local states around a finite mean value, are presented
A state-space approach to the design of syndrome formers
No full textIn this paper the syndrome generation problem is analysed from a state-space point of view. The original problem, formulated in a system theory context, is translated into algebraic terms and proved to be equivalent to the solvability of a polynomial matrix equation.
A complete description of all solutions and, in particular, of all “minimal” solutions is also provided
State observers for discrete time linear systems with unknown inputs
No full textIn the paper the problem of designing a full-order state
observer for a general discrete-time linear system with unknown inputs
is analyzed. Necessary and sufficient conditions for the existence either of
an asymptotic or of a deadbeat observer are provided, and a constructive
design procedure, together with some examples, are discussed. Finally, the
equivalence of these conditions for problem solvability with those derived
in previous contributions by means of different approaches is explicitly
proved
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