27,381 research outputs found
A note on stability conditions for planar switched systems
This paper is concerned with the stability problem for the planar linear
switched system , where the real
matrices are Hurwitz and is a measurable function. We give coordinate-invariant
necessary and sufficient conditions on and under which the system
is asymptotically stable for arbitrary switching functions . The new
conditions unify those given in previous papers and are simpler to be verified
since we are reduced to study 4 cases instead of 20. Most of the cases are
analyzed in terms of the function \Gamma(A_1,A_2)={1/2}(\tr(A_1) \tr(A_2)-
\tr(A_1A_2)).Comment: 9 pages, 3 figure
Stability criteria for planar linear systems with state reset
In this work we perform a stability analysis for a class of switched linear systems, modeled as hybrid automata. We deal with a switched linear planar system, modeled by a hybrid automaton with one discrete state. We assume the guard on the transition is a line in the state space and the reset map is a linear projection onto the x-axis. We define necessary and sufficient conditions for stability of the switched linear system with fixed and arbitrary dynamics in the location. \u
Geometry of the Limit Sets of Linear Switched Systems
The paper is concerned with asymptotic stability properties of linear
switched systems. Under the hypothesis that all the subsystems share a non
strict quadratic Lyapunov function, we provide a large class of switching
signals for which a large class of switched systems are asymptotically stable.
For this purpose we define what we call non chaotic inputs, which generalize
the different notions of inputs with dwell time. Next we turn our attention to
the behaviour for possibly chaotic inputs. To finish we give a sufficient
condition for a system composed of a pair of Hurwitz matrices to be
asymptotically stable for all inputs
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