Discretisation And Control Of Polytopic Systems With Uncertain Sampling Rates And Network-induced Delays

This paper investigates the problems of uncertain sampling rate discretisation and the networked control of uncertain time-invariant continuous-time linear systems in polytopic domains. The sampling period is assumed to be unknown but belonging to a given interval. To avoid the difficulty of dealing with the exponential of uncertain matrices, a discrete-time model is obtained by applying a Taylor series expansion of degree ℓ to the original system. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, called a multi-simplex, plus an additive norm-bounded term representing the discretisation residual error. The original continuous-time system is controlled through a communication network that introduces a time delay in the process. Linear matrix inequality relaxations that include a scalar parameter search are proposed for the design of a digital robust state feedback controller that guarantees the closed-loop stability of the networked control system. Numerical experiments are presented to illustrate the versatility of the proposed method, which can be applied to a more general class of networked control problems than the existing approaches in the literature. © 2014 © 2014 Taylor & Francis