  The problem of designing a stabilizing feedback controller in the presence of
saturating actuators and multi-rate (asynchronous) aperiodic state measurements
is studied. Specifically, we consider a scenario in which measurements of the
plant states are collected at the controller end in a sporadic and asynchronous
fashion. A hybrid controller is used to perform a fusion of measurements
sampled at different times. In between sampling events, the controller behaves
as a copy of the plant and provides a feedback control signal based on the
reconstruction of the plant state. The presence of saturation at the plant
input limits the value of the components of this signal to a bounded range.
When a new measurement is available, the controller state undergoes an
instantaneous jump. The resulting system is augmented with a set of timers
triggering the arrival of new measurements and analyzed in a hybrid systems
framework. Relying on Lyapunov tools for hybrid systems and techniques for
control design under saturation, we propose sufficient conditions in the form
of matrix inequalities to ensure regional exponential stability of a closed-set
containing the origin of the plant, i.e., exponential stability with a
guaranteed region of attraction. Specifically, explicit estimates of the basin
of attraction are provided in the form of ellipsoidal sets. Leveraging those
conditions, a design procedure based on semidefinite programming is proposed to
design a stabilizing controller with maximized size of the basin attraction.
The effectiveness of the proposed methodology is shown in an example.
