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

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-

Characterization of well-posedness of piecewise linear systems

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Caratheodory. The concepts of jump solutions or of sliding modes are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multimodal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-pose

Characterization of well-posedness of piecewise linear systems

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\'eodory. The concepts of jump solutions or a sliding mode are not considered here. In this sense, the problem to be discussed is one of the most basic problems in the study of well-posedness for discontinuous dynamical systems. First, we derive necessary and sufficient conditions for bimodal systems to be well-posed, in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Next, its extensions to the multi-modal case are discussed. As an application to switching control, in the case that two state feedback gains are switched according to a criterion depending on the state, we give a characterization of all admissible state feedback gains for which the closed loop system remains well-posed. \u

Bifurcation diagram for saddle/source bimodal linear dynamical systems

We continue the study of the structural stability and the bifurcations of planar bimodal linear dynamical systems (BLDS) (that is, systems consisting of two linear dynamics acting on each side of a straight line, assuming continuity along the separating line). Here, we enlarge the study of the bifurcation diagram of saddle/spiral BLDS to saddle/source BLDS and in particular we study the position of the homoclinic bifurcation with regard to the new improper node bifurcationPostprint (published version