Stability analysis of networked control systems: A sum of squares approach

Abstract

Abstract-This paper presents a sum of squares (SOS) approach to the stability analysis of networked control systems (NCSs) incorporating time-varying delays and time-varying transmission intervals. We will provide mathematical models that describe these NCSs and transform them into suitable hybrid systems formulations. Based on these hybrid systems formulations we construct Lyapunov functions using SOS techniques that can be solved using LMI-based computations. This leads to several advantages: (i) we can deal with nonlinear polynomial controllers and systems, (ii) we can allow for nonzero lower bounds on the delays and transmission intervals in contrast with various existing approaches, (iii) we allow more flexibility in the Lyapunov functions thereby possibly obtaining improved bounds for the delays and transmission intervals than existing results, and finally (iv) it provides an automated method to address stability analysis problems in NCS.

Stability analysis of networked control systems: A sum of squares approach

“…Next to a reduction in conservatism, our method offers various other advantages with respect to existing approaches, such as dealing with non-zero lower bounds on varying delays and transmission intervals, dealing with nonlinear (polynomial) plants and controllers, not requiring an overapproximation of the NCS (as needed in the discrete-time approach) and finally, the SOS-based approach offers an automated method to tackle the stability problem for NCS including varying delays and transmission intervals. Interestingly, the consideration of communication constraints and network protocols is also possible in the presented framework using the general NCS models in [13], see the extended version [1] of this paper for details. Actually it is shown in [1], for the NCS benchmark example of the batch reactor, that this SOS-based approach provides improved bounds for the delays and transmission intervals compared to the recent results in [13].…”

“…Interestingly, the consideration of communication constraints and network protocols is also possible in the presented framework using the general NCS models in [13], see the extended version [1] of this paper for details. Actually it is shown in [1], for the NCS benchmark example of the batch reactor, that this SOS-based approach provides improved bounds for the delays and transmission intervals compared to the recent results in [13].…”

“…For the sake of brevity, we will not consider communication constraints and network protocols, which is also possible based on the general NCS model discussed in [13] which extends earlier work [20], inspired by [27]. In the extended version [1] of this paper, this general setup and the usage of SOS techniques for the stability analysis of NCSs including these communication constraints is discussed.…”

Exploring the Boundaries of Robust Stability Under Uncertain Communication: An NCS Toolbox Applied to a Wireless Control Setup

“…Some researchers focused on the case where stochastic information is included in models for delays and transmission intervals [4], [20], [47], [60], [63]- [65]. Other researchers have focused on the "probability distribution free" case in [6], [15], [16], [21], [27], [28], [31], [49], [50], [68], and [72]. In the latter case, the time-varying and uncertain transmission intervals and transmission delays are taken from a bounded set, without presuming any knowledge on the particular probability distribution on this bounded support.…”

Adaptive gain-order fractional control for network-based applications

“…[32,33,34] and references therein). In this paper, taking into account that NCSs can be tackled as switching systems [35], the stability problem will be analyzed on the basis of switching systems -refer to [36,37] for some advantages of this treatment.…”