Feedback Passivation of Discrete-Time Systems Under Communication Constraints

Passivity is a desirable property of a dynamical system because it implies stability and is invariant under negative feedback and parallel interconnections. Feedback passivation is the process of making a nonpassive system passive through feedback control. In this technical note, we study the problem of feedback passivation when the controller has limited information about the state of the plant. Nonlinear plants that are linear in the control inputs are considered. The main result of the technical note is a certainty equivalence principle: any state feedback controller that ensures closed-loop input-strict passivity with index μ using the exact state of the plant will also ensure closed-loop stochastic quasi passivity using an estimate of the state, provided that the infinity norm of the estimation error process is bounded by some function of μ. A corollary is that for linear systems, although passivity is more strict than stability, feedback passivation does not place more constraints on the estimation error and hence does not demand more from the communication channel than mean square stabilization.