Integral-Input-to-State Stabilization of Switched Nonlinear Systems with a Cyclic Switching Policy
by
Wenxiang Xie
Nanyang Technological University, Singapore
Coauthors: Changyun Wen (Nanyang Technological University, Singapore), Zhengguo Li (Nanyang Technological University, Singapore)

Our previous work studied the integral-input-to-state stabilization of switched nonlinear systems under such assumptions that each subsystem of the considered switched nonlinear system is integral- input-to-state stable (IISS), or not IISS in the whole state space but in a region. This is due to for a single nonlinear system, many research results on integral-input-to-state stability are available. In this paper, we consider the integral-input-to-state stabilization of a class of switched nonlinear systems with a cyclic switching policy of system modes.

The considered system consists of IISS subsystems (i.e., the continuous states must eventually be small if the integrals of the corresponding inputs are small) and subsystems whose continuous states may eventually be infinite even if the integrals of the corresponding inputs are small. For the latter, we analyze their properties.

Then, based on such properties we prove that the considered switched nonlinear system can be integral-input-to-state stabilized under some proper conditions.

Date received: January 27, 2000