Power Spectral Analysis of Networked Control Systems With Data Dropouts

Abstract

It can be verified that the system (21) does not satisfy the condition of [4] and, hence, no conclusion on the global asymptotic stability can be drawn based on the results of [4]. However, by using Algorithm 3, it can be verified that the condition of Theorem 2 is satisfied with P = 0:5643 00:3214 02:5945We thus conclude that (21) is globally asymptoticallystable at the origin. A trajectory is shown in Fig. 4. IV. CONCLUSIONIn this note, we established simple conditions under which linear systems defined on a closed hypercube and linear systems with partial state saturation are globally asymptotically stable at the origin. These conditions were shown to be less conservative than the existing conditions. Based on these conditions, iterative LMI algorithms are proposed for verifying global asymptotic stability of these systems. Numerical examples were used to show the effectiveness of the proposed algorithms. REFERENCES[1] S.

Packetized Predictive Control of Stochastic Systems Over Bit-Rate Limited Channels With Packet Loss

“…Remark 6: Lemma 7 and Theorem 4 generalize results of [24], [50], [56]. To be more precise, whereas in the papers mentioned above only NCS's with a packet-dropping network carrying scalar signals are considered, the results in the present work are applicable to PPCs with N ≥ 1, i.e., where sequences of plant inputs are transmitted.…”

“…The above lemma gives maximum dropout-rates which preserve stability in terms of Kronecker products. Unfortunately, for large horizon lengths N or plant orders n, evaluating (24) becomes computationally infeasible, due to the need to invert and find eigenvalues of matrices of large dimensions, which often are ill-conditioned. (The matrix U ⊗ U has (N + n)…”

“…Motivated by Statement 5) of Theorem 2 and the approach used in [24] and [56] for NCS's with scalar transmission, we can derive sufficient conditions for stability of the NCS as stated in Lemma 7. To state this result, we first require a more general characterization which gives sufficient (but not necessary) conditions of MSS and AWSS of the NCS.…”

“…In the semi-definite case Θ 0, sufficiency of (29) can be proven following an idea akin to that used, e.g., in [24]. We first recall that A(p) is Schur, iff for some Ω 0 it holds that:…”

Data Transmission Over Networks for Estimation and Control

“…Preliminary work in this area has concentrated on networks consisting of a single link between the sensor and the remote estimator/controller. Within the one-link framework, both the stability [19], [23] and the performance [15], [19] have been analyzed. Approaches to compensate for the data loss to counteract the degradation in performance have also been proposed [9], [15], [16], [21].…”