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  • Artículo de Publicación Periódica
    Characterization of integral input-to-state stability for nonlinear time-varyng systems of infinite dimension
    (2022) Mancilla Aguilar, Jose Luis; Rojas Ruiz, Jose; Haimovich, Hernan
    For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded-energy input/bounded state (UBEBS) is established under a reasonable assumption of continuity of the trajectories with respect to the input, at the zero input. By particularizing to specific instances of infinite-dimensional systems, such as time-delay, or semilinear over Banach spaces, sufficient conditions are given in terms of the functions defining the dynamics. In addition, it is also shown that for semilinear systems whose nonlinear term satisfies an affine-in-the-state norm bound, it holds that iISS becomes equivalent to just 0-GUAS, a fact known to hold for bilinear systems. An additional important aspect is that the iISS notion considered is more general than the standard one.
  • Artículo de Publicación Periódica
    Some results for switched homogeneous systems
    (2016) Mancilla Aguilar, Jose Luis; García Galiñanes, Rafael
    "In this paper, we prove the equivalence of weak attractivity, attractivity, global uniform asymptotic stability and exponential stability of switched homogeneous systems whose switching signals verify a certain property P. In addition we show that these stability properties imply that the system stability is robust with respect to disturbances in a power-like sense, which comprises both, the exponential ISS and iISS."
  • Artículo de Publicación Periódica
    Incompressible flow modeling using an adaptive stabilized finite element method based on residual minimization
    (2021) Kyburg, Felix E.; Rojas, Sergio; Caloa, Victor M.
    "We model incompressible Stokes flows with an adaptive stabilized finite element method, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers a robust error estimator to guide mesh adaptivity. We analyze the accuracy of different discrete velocity-pressure pairs of continuous finite element spaces, which do not necessarily satisfy the discrete inf-sup condition. We validate the framework's performance with numerical examples."
  • Artículo de Publicación Periódica
    (Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization
    (2021) Mancilla-Aguilar, J. L.; Haimovich, Hernán
    "It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input."
  • Artículo de Publicación Periódica
    Uniform input-to-state stability for switched and time-varying impulsive systems
    (2020-12) Mancilla-Aguilar, J. L.; Haimovich, Hernán
    "We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and time-varying, switched and nonswitched, impulsive and nonimpulsive systems in several directions."