11,189 research outputs found
State dependent switching control of affine linear systems with dwell time: application to power converters
This paper addresses a state dependent switching law for the stabilization of continuous-time, switched affine linear systems satisfying dwell time constraints. Such a law is based on the solution of Lyapunov-Metzler inequalities from which stability conditions are derived. The key point of this law is that the switching rule calculation depends on the evolution forward by the dwell time of quadratic Lyapunov functions assigned to each subsystem. As such, the proposed law is readily applicable to power converters showing that it is an interesting alternative to other switching control techniques
On feedback stabilization of linear switched systems via switching signal control
Motivated by recent applications in control theory, we study the feedback
stabilizability of switched systems, where one is allowed to chose the
switching signal as a function of in order to stabilize the system. We
propose new algorithms and analyze several mathematical features of the problem
which were unnoticed up to now, to our knowledge. We prove complexity results,
(in-)equivalence between various notions of stabilizability, existence of
Lyapunov functions, and provide a case study for a paradigmatic example
introduced by Stanford and Urbano.Comment: 19 pages, 3 figure
Quantized Feedback Stabilization of Sampled-Data Switched Linear Systems
We propose a stability analysis method for sampled-data switched linear
systems with quantization. The available information to the controller is
limited: the quantized state and switching signal at each sampling time.
Switching between sampling times can produce the mismatch of the modes between
the plant and the controller. Moreover, the coarseness of quantization makes
the trajectory wander around, not approach, the origin. Hence the trajectory
may leave the desired neighborhood if the mismatch leads to instability of the
closed-loop system. For the stability of the switched systems, we develop a
sufficient condition characterized by the total mismatch time. The relationship
between the mismatch time and the dwell time of the switching signal is also
discussed.Comment: 17 pages, 3 figure
Data-driven control of switched linear systems with probabilistic stability guarantees
This paper tackles state feedback control of switched linear systems under
arbitrary switching. We propose a data-driven control framework that allows to
compute a stabilizing state feedback using only a finite set of observations of
trajectories with quadratic and sum of squares (SOS) Lyapunov functions. We do
not require any knowledge on the dynamics or the switching signal, and as a
consequence, we aim at solving \emph{uniform} stabilization problems in which
the feedback is stabilizing for all possible switching sequences. In order to
generalize the solution obtained from trajectories to the actual system,
probabilistic guarantees on the obtained quadratic or SOS Lyapunov function are
derived in the spirit of scenario optimization. For the quadratic Lyapunov
technique, the generalization relies on a geometric analysis argument, while,
for the SOS Lyapunov technique, we follow a sensitivity analysis argument. In
order to deal with high-dimensional systems, we also develop parallelized
schemes for both techniques. We show that, with some modifications, the
data-driven quadratic Lyapunov technique can be extended to LQR control design.
Finally, the proposed data-driven control framework is demonstrated on several
numerical examples.Comment: This is an extended version to the previous pape
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