614 research outputs found
A looped-functional approach for robust stability analysis of linear impulsive systems
A new functional-based approach is developed for the stability analysis of
linear impulsive systems. The new method, which introduces looped-functionals,
considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid
of exponential terms. This allows one to easily formulate dwell-times results,
for both certain and uncertain systems. It is also shown that this approach may
be applied to a wider class of impulsive systems than existing methods. Some
examples, notably on sampled-data systems, illustrate the efficiency of the
approach.Comment: 13 pages, 2 figures, Accepted at Systems & Control Letter
Time-triggered and event-triggered control of switched affine systems via a hybrid dynamical approach
This paper focuses on the design of both periodic time- and event-triggered
control laws of switched affine systems using a hybrid dynamical system approach. The novelties of this paper rely on the hybrid dynamical representation
of this class of systems and on a free-matrix min-projection control, which relaxes the structure of the usual Lyapunov matrix-based min-projection control.
This contribution also presents an extension of the usual periodic time-triggered
implementation to the event-triggered one, where the control input updates are
permitted only when a particular event is detected. Together with the definition
of an appropriate optimization problem, a stabilization result is formulated to
ensure the uniform global asymptotic stability of an attractor for both types of
controllers, which is a neighborhood of the desired operating point. Finally, the
proposed method is evaluated through a numerical example.Agence Nationale de la Recherche (ANR)France Grant ANR-18-CE40-0022-01Agencia Estatal de Investigación (AEI)-Spain Grant PID2019-105890RJ-10
Discrete and intersample analysis of systems with aperiodic sampling
International audienceThis article addresses the stability analysis of linear time invariant systems with aperiodic sampled-data control. Adopting a difference inclusion formalism, we show that necessary and sufficient stability conditions are given by the existence of discrete-time quasi-quadratic Lyapunov functions. A constructive method for computing such functions is provided from the approximation of the necessary and sufficient conditions. In practice, this leads to sufficient stability criteria under LMI form. The inter-sampling behavior is discussed there: based on differential inclusions, we provide continuous-time methods that use the advantages of the discrete-time approach. The results are illustrated by numerical examples that indicate the improvement with regard to the existing literature
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