Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

Abstract EN

The state estimation problem for a class of switched linear systems which only switches in some short interval is addressed.

Besides the asymptotic stability of error dynamics, the boundness of error state is a significant issue for short-time switched systems.

By introducing the concept of finite-time stability, the state estimation procedure is formulated to determine appropriate observer gains ensuring the error dynamics is finite-time stable in the short-time switching intervals of interest.

Optimal finite-time observers are designed through iterative algorithms to minimize the bound of error state, in the cases with and without disturbances.

Particularly, when the total activation time is known, a less conservative result can be derived and an optimization problem can be solved with the help of the genetic algorithm.

A numerical example is provided to illustrate the theoretical findings in this paper.