Robust state derivative feedback LMI-based designs for discretized systems.

Abstract

This work addresses novel Linear Matrix Inequality (LMI)-based conditions for thedesign of discrete-time state derivative feedback controllers. The main contribution of this work consists of an augmented discretized model formulated in terms of the state derivative, such that uncertain sampling periods and parametric uncertainties in polytopic form can be propagated from the original continuous-time state space representation. The resulting discrete-time model is composed of homogeneous polynomial matrices with parameters lying in the Cartesian product of simplexes, plus an additive norm-bounded term representing the residual discretization error. Moreover, the referred condition allows for the closed-loop poles allocation of the augmented system in a D-stable region. Finally, numerical simulations illustrate the effectiveness of the proposed method.

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network‐induced delay

“…and (44) can be rewritten as (34) with polynomial homogeneous matrices given by (36), which implies that discretized model (12) (37). As aforementioned, the computation of the exact values for the residuals is a hard task.…”

“…Taking into account Lemma 3, the parameter-dependent matrices Ξ(𝛼) in (31) can also be recast in terms of homogeneous polynomial matrices Ξ [g] (𝛼). For the matrices Ξ[g] (𝛼) and Ξ[g] (𝛼), a detailed formulation is given in Leandro et al [37], where the later can be found by replacing T(𝛼 2 ) with T(𝛼 2 ). As a consequence, the homogeneous polynomial matrix Ξ[g] (𝛼) is then presented here for clarity…”

“…In Theorem 2 context, the proof is based on the same ideas and will be omitted herein. Following the proof presented in Leandro et al [37], for any 𝛼 ∈ (Λ N 1 × Λ 2 ), a sampling period T(𝛼 2 ) and a network-induced delay τ, the solution of (30) by means of the augmented model (20) over the interval t ∈ [ kT(𝛼 2 ) + , (k + 1)T(𝛼 2 ) ] is given by:…”