On controller-driven varying-sampling-rate stabilization via Lie-algebraic solvability

Abstract

Control systems involving shared communications networks are becoming ubiquitous. The inclusion of a communications network within a feedback loop imposes new control challenges. We consider a setting where a centralized controller/scheduler is in charge of the control of several processes and also of administering access to the shared communications network. In this setting, the controller may perform on-line variations of the sampling rate of all processes in order to accommodate for new processes requiring access to the network and to maximize performance when processes finish operation. We refer to this setting as controller-driven varying-sampling-rate (VSR). We regard a continuous-time system sampled at varying rates as a discrete-time switched system (DTSS), and aim at devising sampling-rate dependent feedback to ensure stability irrespective of the way in which the sampling rate is varied. Our feedback design strategy is based on Lie-algebraic solvability. The current paper presents two main contributions: a) it demonstrates that control design based on Lie-algebraic solvability is much less restrictive when applied to the controller-driven VSR setting than when applied to DTSSs of arbitrary form, and b) we give sufficient conditions for the stabilizability of the VSR-DTSS by means of the Lie-algebraic-solvability condition. As opposed to previous results, these sufficient conditions do not impose a restriction on the number of subsystems of the DTSS.