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D-stability under channel capacity constraints
Date Issued
01-07-2019
Author(s)
Rokade, Kiran
Indian Institute of Technology, Madras
Abstract
We address the problem of stabilizing a system, with a certain desired dynamic performance, using control signal sent over a communication channel having a limited capacity. A desired dynamic performance of the closed-loop system is obtained by placing its poles in a specific region of the open left-half of the complex plane. Denoting such a region by D, this procedure is also called V-stabilization. We first analyze a single-input linear time-invariant (LTI) system with state-feedback control over a channel subjected to additive noise. Using tools from H2control theory, we pose the above stabilization problem as an optimization problem involving linear matrix inequalities (LMIs). Using this, we derive a sufficient condition for V-stabilization of the system subject to the channel capacity constraint. Further, we extend our analysis to a multi-input LTI system with state-feedback over a multi-input multi-output (MIMO) channel subjected to additive noise. The channel consists of multiple single-input single-output (SISO) subchannels connected in parallel. The total capacity of the MIMO channel is fixed, while the individual subchannel capacities can be freely allocated. We provide a necessary and sufficient condition for stabilization and a sufficient condition for V-stabilization of this system subject to the channel capacity constraints. We also propose a method to design the channel and an optimal controller.
Volume
2019-July