Stabilization of Networked Control Systems with Hyper-Sampling Periods

Abstract

This chapter considers the stabilization of Networked Control Systems (NCSs) under the hyper-sampling mode. Such a sampling mode, recently proposed in the literature, appears naturally in the scheduling policies of real-time systems under constrained (calculation and communication) resources. Meanwhile, as expected, the stabilization problem under the hyper-sampling mode is much more complicated than in the case of single-sampling mode. In this chapter, we propose a procedure to design the feedback gain matrix such that we can obtain a stabilizable region as large as possible. In the first step, we determine the stabilizable region under the singlesampling period. This step can be easily obtained by solving some linear matrix inequalities (LMIs) and from the result we may obtain a stabilizable region for the hyper-sampling period. Then, in the second step, we further detect the stabilizable region, based on the one found in the first step, by adjusting the feedback gain matrices based on the asymptotic behavior analysis. By this step, a larger stabilizable region may be found and this step can be used in an iterative manner. The proposed procedure will be illustrated by a numerical example. We can see from the example that the stabilizable region under the hyper-sampling period may lead to a smaller average sampling frequency (ASF) guaranteeing the stability of the NCS than the single-sampling period, i.e., less system resources are required by the hyper-sampling period.