Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter

Abstract

The paper addresses the problem of designing a stabilizing control for switched affine and its experimental verification based on Linear Matrix Inequalities (LMIs). The main contribution is on the determination of a switching function that exploits the potential of LMI control approaches and which assures global stability and minimizes a guaranteed quadratic cost. Slack variables are introduced to reduce the design conservatism and new sufficient LMI conditions for the synthesis of the controllers are presented. Thus, it is showed that the performance of the control system is superior with a smaller guaranteed cost upper bound of that afforded by recent results. In addition, a theorem with sufficient conditions for the control of switched affine systems that allows a way to garantee a bounded sample time rate on the switching function is proposed. The implementation of the switching function taking into account a bounded sampling time is analysed and discussed with particular interest. Finally, the theoretical results are applied to Buck DC-DC converter. Several simulations show the usefulness of the methodology and experimental results obtained from a prototype validate this approach.