Characterization of a Family of Controllers for Networked Systems Under Nonuniform Communication and Network-Induced Delay

Abstract

In this note, we characterize a family of discrete-time strictly causal stabilizing controllers for networked systems under nonuniform communication and network-induced delays. First, we absorb the feedback delay in the controller structure and parameterize a family of stabilizing controllers for the delay-free plant with some restrictions on the controller structure due to time delay. Then we lift the feedback connection and choose the free parameter of the family in the lifted domain to incorporate the effect of nonuniform communication, resulting in a family of stabilizing controllers under nonuniform communication and delay. Further, we propose a network-friendly architecture that, contrary to existing results, does not require computing a control sequence at the sensor side of the controller and is robust against network packet dropouts. Furthermore, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{2}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> optimization are discussed. Finally, examples of a stabilizing controller and an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> controller illustrate the effectiveness of the proposed techniques.