206 research outputs found
Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes
We aim at studying approximate null-controllability properties of a
particular class of piecewise linear Markov processes (Markovian switch
systems). The criteria are given in terms of algebraic invariance and are
easily computable. We propose several necessary conditions and a sufficient
one. The hierarchy between these conditions is studied via suitable
counterexamples. Equivalence criteria are given in abstract form for general
dynamics and algebraic form for systems with constant coefficients or
continuous switching. The problem is motivated by the study of lysis phenomena
in biological organisms and price prediction on spike-driven commodities.Comment: Mathematics of Control, Signals, and Systems, Springer Verlag
(Germany), 2015, online first
http://link.springer.com/article/10.1007/s00498-015-0146-
Stability and controllability of planar bimodal linear complementarity systems
The object of study of this paper is the class of hybrid systems consisting of so-called linear complementarity (LC) systems, that received a lot of attention recently and has strong connections to piecewise affine (PWA) systems. In addition to PWA systems, some of the linear or affine submodels of the LC systems can ‘live’ at lower-dimensional subspaces and re-initializations of the state variable at mode changes is possible. For LC systems we study the stability and controllability problem. Although these problems received for various classes of hybrid systems ample attention, necessary and sufficient conditions, which are explicit and easily verifiable, are hardly found in the literature. For LC systems with two modes and a state dimension of two such conditions are presented
On the controllability of bimodal piecewise linear systems
This paper studies controllability of bimodal systems that consist of two linear dynamics on each side of a given hyperplane. We show that the controllability properties of these systems can be inferred from those of linear systems for which the inputs are constrained in a certain way. Inspired by the earlier work on constrained controllability of linear systems, we derive necessary and sufficient conditions for a bimodal piecewise linear system to be controllable.Natl Sci Fdn; Univ Penn, Sch Engn & Appl Sci
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