Decentralized Control of Switched-Systems with Path-Dependent $\ell_{2}$-induced Bounds

Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

“…In this article, we provide proofs for the results presented in [22] and [23]. In the work developed in [19]- [23], the synthesis problem requires the number of switching paths and the number of coupled LMI equations to be the same. In this article, we develop synthesis results for the case where we have a smaller number of decision variables than the full cardinality of the admissible sequence set by using basis functions.…”

“…as in (23). Furthermore, rank conditions above are always satisfied when n K i ≥ n, leaving us with LMIs (a)-(c).…”

“…The synthesis results for a decentralized controller for nested systems with finite memory were presented in [21]. The decentralized controller synthesis was extended to include access to finite future modes in [22], and path-dependent performance bounds were considered in [23]; these papers form the basis for the theoretical work presented here. In this article, we provide proofs for the results presented in [22] and [23].…”

“…The decentralized controller synthesis was extended to include access to finite future modes in [22], and path-dependent performance bounds were considered in [23]; these papers form the basis for the theoretical work presented here. In this article, we provide proofs for the results presented in [22] and [23]. In the work developed in [19]- [23], the synthesis problem requires the number of switching paths and the number of coupled LMI equations to be the same.…”