${L}_{2}$-Stability Criterion for Systems with Decentralized Asynchronous Controllers

Abstract

This paper deals with the stability analysis of decentralized sampled-data Linear Time Invariant (LTI) control systems with asynchronous sensors and actuators. We consider the case where each controller in the decentralized setting has its own sampling and actuation frequency which translates to asynchrony between sensors and actuators. The errors induced due to sampling and asynchronicity are modelled using two different operator approaches, leading to simple L2stability criteria for the overall decentralized control system. The simplicity of the obtained criteria is illustrated by an example and simulation results exhibit the effectiveness of the approach.

Frequency-domain stability conditions for asynchronously sampled decentralized LTI systems

“…In other words, we study the effect of asynchrony between local, possibly aperiodic, sampled-data controllers, on the overall stability of the system. The significance of such an analysis is corroborated using the following example studied in [24]. Consider the decentralized LTI system defined by…”

“…Feedback interconnections of this form, shown in Figure 5, are often studied in the robust control framework. This representation aids in providing simple L 2 -stability criteria as we have shown in [24]. In the next section, we illustrate the implication of such L 2 -stability properties on the exponential stability of the decentralized LTI system ( 13)-( 16).…”

“…In a previous conference paper [24], we have used the Input-output approach to provide easy-to-check L 2stability conditions for a setting similar to the one considered in this paper. However, the results in [24] only established boundedness and did not take into account individual bounds on sampling and actuation frequencies, thereby leading to considerably more conservative results.…”

“…In a previous conference paper [24], we have used the Input-output approach to provide easy-to-check L 2stability conditions for a setting similar to the one considered in this paper. However, the results in [24] only established boundedness and did not take into account individual bounds on sampling and actuation frequencies, thereby leading to considerably more conservative results. Here, in this paper, we propose a novel approach that guarantees exponential stability of the state-space model by taking into account individual bounds on sampling and actuation frequencies, which ensures that the results in this paper are less conservative and more generic in comparison to the results in [24].…”

Investigating new classes of sampling sequences: Application to the stability analysis of decentralized sampled-data systems

“…Using the same hybrid framework as [11], [12] shows stability of unsynchronized saturated linear systems. In [13] and [14] small gain arguments are used to establish stability of decentralized sampled-data systems while [15] use integral quadratic constraints to achieve the same objective.…”