105 research outputs found
Realization Theory for LPV State-Space Representations with Affine Dependence
In this paper we present a Kalman-style realization theory for linear
parameter-varying state-space representations whose matrices depend on the
scheduling variables in an affine way (abbreviated as LPV-SSA representations).
We deal both with the discrete-time and the continuous-time cases. We show that
such a LPV-SSA representation is a minimal (in the sense of having the least
number of state-variables) representation of its input-output function, if and
only if it is observable and span-reachable. We show that any two minimal
LPV-SSA representations of the same input-output function are related by a
linear isomorphism, and the isomorphism does not depend on the scheduling
variable.We show that an input-output function can be represented by a LPV-SSA
representation if and only if the Hankel-matrix of the input-output function
has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension
of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart
of partial realization theory for LPV-SSA representation and prove correctness
of the Kalman-Ho algorithm. These results thus represent the basis of systems
theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as
follows: typos have been fixe
Discrete Time Systems
Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area
On the Herdability of Linear Time-Invariant Systems with Special Topological Structures
In this paper, we investigate the herdability property, namely the capability
of a system to be driven towards the (interior of the) positive orthant, for
linear time-invariant state-space models. Herdability of certain matrix pairs
(A,B), where A is the adjacency matrix of a multi-agent network, and B is a
selection matrix that singles out a subset of the agents (the "network
leaders"), is explored. The cases when the graph associated with A, G(A), is
directed and clustering balanced (in particular, structurally balanced), or it
has a tree topology and there is a single leader, are investigated.Comment: Provisionally accepted in Automatica, currently under review. arXiv
admin note: substantial text overlap with arXiv:2108.0157
Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis
Magdeburg, Univ., Fak. fĂĽr Elektrotechnik und Informationstechnik, Diss., 2015von Philipp Rumschinsk
On the stability, stabilizability and control of certain classes of Positive Systems
In this thesis stability, stabilizability and other control issues for certain classes of Positive Systems are investigated. In the first part, the focus is on Compartmental Systems: we start from Compartmental Switched Systems and show that, with respect to the general class of Positive Switched Systems, a much clearer picture of stability under arbitrary switching, stability under persistent switching, and stabilizability (where the control action may either pertain the switching function or involve the design of feedback controllers) can be drawn. Secondly, for the class of Compartmental Multi-Input Systems the problem of designing a state-feedback matrix that preserves the compartmental property of the resulting closed-loop system, meanwhile achieving asymptotic stability is addressed. Such an analysis finally leads to the development of an algorithm that allows to assess problem solvability and provides a possible solution whenever it exists. The second part of the thesis is devoted to the Positive Consensus Problem: for a homogeneous Positive Multi-Agent System we investigate the problem of determining a state-feedback law that can be individually implemented by each agent, preserves the positivity of the overall system, and leads to the achievement of consensus. Finally, for a particular class of Positive Bilinear Systems that arises in drugs concentration design for HIV treatment, we address the problem of determining an optimal constant input that stabilizes the system while maximizing its robustness against the presence of the external disturbance
- …