Seminar Details
2024-05-21 (14h) : Stability and Performance of Discrete-Time Switched Nonlinear Systems
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Grace Deaecto (Unicamp and Imperial College London)
Abstract :
Switched systems are composed of a set of subsystems and a rule (or function) to orchestrate
the switching among them. They present interesting theoretical properties and a wide range of
applications in many different areas of the science. In this talk, our goal is to study the stabilisation
problem for discrete-time switched nonlinear systems under two different scenarios: time-dependent
switching function (open-loop control) and state-dependent switching function (closed-loop control).
In the first, we consider that the switching function is subjected to persistent dwell time and in the
second it is a state-dependent control variable to be designed. In both cases, the goal is to ensure
global exponential stability of the zero equilibrium and a guaranteed performance for the overall
system. A numerical method that applies to a class of switched polynomial systems is proposed to
validate the results. This is able to check locally the sufficient conditions through LMI conditions
and takes into account the maximisation of an ellipsoidal set for which any trajectory starting from
it does not leave the stability region. Academic examples are used to illustrate the main features of
the proposed methodologies.