3 research outputs found
Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems
This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches
Strong exponential stability of switched impulsive systems with mode-constrained switching
Strong stability, defined by bounds that decay not only over time but also
with the number of impulses, has been established as a requirement to ensure
robustness properties for impulsive systems with respect to inputs or
disturbances. Most existing results, however, only consider weak stability. In
this paper, we provide a method for calculating the maximum overshoot and the
decay rate for strong (and weak) global uniform exponential stability bounds
for non-linear switched impulsive systems. We consider the scenario of
mode-constrained switching where not all transitions between subsystems are
allowed, and where subsystems may exhibit unstable dynamics in the flow and
jump maps. Based on direct and reverse mode-dependent average dwell-time and
activation-time constraints, we derive stability bounds that can be improved by
considering longer switching sequences for computation. We provide numerical
examples that illustrate the weak and strong exponential stability bounds and
also how the results can be employed to ensure the stability robustness of
nonlinear systems that admit a global state weak linearization.Comment: 23 pages, 4 figure