Robust Wireless Servo Control Using a Discrete-Time Uncertain Markovian Jump Linear Model

Abstract

This brief proposes a robust control synthesis technique for wireless servo applications modeled as an uncertain discrete-time Markovian jump linear system. It is desired to find mean square stabilizing state feedback controllers with upper bounded quadratic cost when the transition probabilities of the Markov chain describing the network conditions, the state space dynamics, and the initial condition are unknown but belong to known convex polytopic sets. Under appropriate assumptions, these parametric uncertainties can be examined simultaneously, and controllers can be synthesized using linear matrix inequalities (LMIs). The LMIs utilize extended parameters to reduce conservativeness due to initial condition and plant uncertainty. The proposed method is used to design and demonstrate a robust wireless servo controller for an inverted pendulum system.