On the stability of planar randomly switched systems
نویسندگان
چکیده
منابع مشابه
On the stability of planar randomly switched systems
Consider the random process (Xt)t>0 solution of Ẋt = AItXt where (It)t>0 is a Markov process on {0, 1} and A0 and A1 are real Hurwitz matrices on R. Assuming that there exists λ ∈ (0, 1) such that (1−λ)A0 + λA1 has a positive eigenvalue, we establish that ‖Xt‖ may converge to 0 or +∞ depending on the the jump rate of the process I. An application to product of random matrices is studied. This p...
متن کاملStability 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...
متن کاملA note on stability conditions for planar switched systems
This paper is concerned with the stability problem for the planar linear switched system ẋ(t) = u(t)A1x(t)+(1−u(t))A2x(t), where the real matrices A1, A2 ∈ R 2×2 are Hurwitz and u(·) : [0,∞[→ {0, 1} is a measurable function. We give coordinate-invariant necessary and sufficient conditions on A1 and A2 under which the system is asymptotically stable for arbitrary switching functions u(·). The ne...
متن کاملStabilizing Randomly Switched Systems
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sur...
متن کاملStability of Planar Switched Systems: the Nondiagonalizable Case
Consider the planar linear switched system ẋ(t) = u(t)Ax(t) + (1− u(t))Bx(t), where A and B are two 2×2 real matrices, x ∈ R, and u(.) : [0,∞[→ {0, 1} is a measurable function. In this paper we consider the problem of finding a (coordinate-invariant) necessary and sufficient condition on A and B under which the system is asymptotically stable for arbitrary switching functions u(.). This problem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2014
ISSN: 1050-5164
DOI: 10.1214/13-aap924