Stability of bimodal planar linear switched systems

Structural Stability of Planar Bimodal Linear Systems

Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spira...

Planar Bimodal Piecewise Linear Systems

exponential stability of uncertain switched linear systems

in this paper, sufficient conditions are proposed to investigate the robust stability of arbitrary switched linear systems with uncertain parameters belongs to the known intervals. in addition, a method is then established to determine the maximum intervals of parameters' variations which guarantee robust exponential stability of uncertain switched linear systems under arbitrary switching. in t...

Stability of Planar Nonlinear Switched Systems

We consider the time-dependent nonlinear system q̇(t) = u(t)X(q(t)) + (1 − u(t))Y (q(t)), where q ∈ R, X and Y are two smooth vector fields, globally asymptotically stable at the origin and u : [0,∞) → {0, 1} is an arbitrary measurable function. Analysing the topology of the set where X and Y are parallel, we give some sufficient and some necessary conditions for global asymptotic stability, uni...

Stabilizer design of planar switched linear systems

This paper considers the stabilization of planar switched linear control systems. First, a structure property of not completely controllable pair (A, b) is revealed. Based on it, a simply verifiable, necessary and sufficient condition for the planar switched linear control system to be feedback stabilizable, is presented under the assumption that the switching law is designable. The proof provi...