Robust Exponential Stability of an Intermittent Transmission State Estimation Protocol

Abstract

The problem of distributed networked sensor agents jointly estimating the state of a plant given by a linear time-invariant system is studied. Each agent can only measure the output of the plant at intermittent time instances, at which times the agent also sends the received plant measurement and its estimate to its neighbors. At each agent, a decentralized observer is attached which utilizes the asynchronous incoming information being sent from its neighbors to drive its own estimate to the state of the plant. We provide sufficient conditions that guarantee global exponential stability of the zero estimation error set. Numerical illustrations are provided. R. G. Sanfelice is with the

State observer with Round-Robin aperiodic sampled measurements with jitter

“…Consider now (29), and use a Schur complement to get e −𝐴 𝜏 𝑃 𝜎 e −𝐴𝜏 − 𝐼 − 𝐾 𝜎 (𝜏)𝐶 𝜎 𝑃 Γ( 𝜎) 𝐼 − 𝐾 𝜎 (𝜏)𝐶 𝜎 > 0, (37) namely 𝑀 (𝜏, 𝜎) > 0, ∀(𝜏, 𝜎) ∈ C. Since C is compact, we may define the scalar (independent of 𝜌):…”

“…𝐴𝜏) instead of Ψ(𝜏) and 𝑌 𝜎 (𝜏) := −𝑃 Γ( 𝜎) 𝐾 𝜎 (𝜏) instead of 𝑌 (𝜏) to show that condition (44) ensures the existence of a gain 𝐾 𝜎 (•) satisfying(29). Secondly, given matrices 𝑃 𝜎 satisfying condition (44), we may follow the steps of Part 2 of the proof of[34, Thm 1] to obtain that (29) holds if, paralleling [34, Eq.…”