Comparison of stability characterisations for networked control systems

Abstract

Abstract-This paper presents linear matrix inequalities for stability analysis for networked control systems (NCSs) that incorporates various network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that may be both smaller and larger than the sampling interval. The problem is approached from a discrete-time modelling perspective. A comparison is made between the use of Parameter Dependent Lyapunov functions and LyapunovKrasovskii functions for stability analysis. Examples illustrate the developed theory.

Constructing a bimodal switched Lyapunov function for non-uniformly sampled-data feedback systems

“…Since it has been pointed out that quadratic stability of T d implies exponential stability of T [28], several methods are proposed for analysis and design for T based on the fact [1], [2], [6], [8], [11], [12], [19], [20], [24]. The following property shown in [9], however, suggests the conservatism of the approach based on quadratic stability: Property 1: The following two conditions are equivalent: (i) T is exponentially stable.…”

“…Improving the approximation by gridding in earlier studies [1], [21], [28], the recent studies take the robustness into account to guarantee the stability. In particular, (i) a robust control approach based on a linear fractional transformation (LFT) uncertainty modeling [6], [8], [24], (ii) a robust control approach based on a polytopic uncertainty modeling [1], [2], [11], [12], and (iii) a robust linear matrix inequality (LMI) approach [19], [20] have been proposed. We note that numerical experiences in the references suggest that these discrete-time approaches are less conservative than other approaches constructing continuous-time Lyapunov functions in, e.g., [4], [5], [7], [14]- [18], [23], [25]- [27].…”

“…Motivated by networked control systems with packet loss (See, e.g., [10]) and embedded control systems with incomplete real-time property (See, e.g., [13]), analysis and design problems for sampled-data systems with uncertainly timevarying sampling intervals have been studied in these days [1], [2], [4]- [9], [11], [12], [14]- [28]. It is obvious that the problems are much harder than those for the standard periodic sampling case, and that robustness plays a crucial role in the study.…”

Networked and quantized control systems with communication delays

“…on the NCS model (12), where m x : R nx → R ≥0 and we will also use the following condition that is only slightly modified with respect to the delay-free conditions in [1]:…”

“…However, up to now, much of the available literature on NCS considers only some of above mentioned types of network phenomena and there is no framework that incorporates all of them. The closest ones (that consider more than 2 of these imperfections) are [20], which consider imperfections of type (i), (iii), (v), [12], [18], [19], which study simultaneously type (ii), (iii), (iv), [21], which focusses on type (ii), (iii), (v) and [2], [5], [9], [10] that consider type (iii), (iv) and (v). Note that some of the mentioned approaches that study varying transmission intervals and/or varying communication delays can be extended to include type (ii) phenomena as well by modeling dropouts as prolongations of the maximal admissible transmission interval (cf.…”