Shared Nonlinear Control in Wireless-Based Remote Stabilization: A Theoretical Approach

Abstract

This paper proposes shared control in wireless-based remote stabilization for nonlinear systems. Shared control that is newly named in this paper can be regarded as simultaneous stabilization of plural nonlinear systems (in different places) by a single (common) controller. This paper consists of two parts. The first part addresses the basis of wireless-based remote stabilization for a single nonlinear system with time-varying delay. We derive a delay-dependent sufficient condition for ensuring the stability of Takagi-Sugeno (T-S) fuzzy models with time-varying delays that are globally (or semiglobally at least) equivalent to nonlinear systems with wireless communication time delays. A feature of the derived condition is to be able to obtain the maximum time delay for ensuring the stability of wireless-based remote control system for given feedback gains. The second part presents shared control of plural nonlinear systems via a single controller. To design a (common) shared controller to stabilize plural nonlinear systems, we derive also a shared control version of the stability condition for T-S fuzzy models with time-varying delays. Design examples demonstrate the utility of this proposed design approach.