Quantised control of nonlinear systems: analysis of robustness to parameter uncertainty, measurement errors, and exogenous disturbances

Abstract

We propose a variant of the recently introduced strategy for stabilisation with limited information by D. Liberzon and J.P. Hespanha and analyse its robustness properties. We show that, if the nominal plant can be made input-to-state stable with respect to measurement errors, parameter uncertainty and exogenous disturbances, then this robustness is preserved with this quantised feedback. More precisely, if a sufficient bandwidth is available on the communication network, then the resulting closed loop is shown to be semiglobally input-to-state practically stable.

Keywords:

• limited-information feedback
• quantisation
• robustness
• nonlinear systems

Notes

1. In a second stage one may think of implementing an adaptive control strategy.

2. We will demonstrate the existence of such Ŵ, by constructing it, in the sequel (cf. Claim 7.1).