Stability Test of Networked Systems with Multiple Delays

In this paper, we propose a sufficient stability condition for networked systems with multiple delays based on the 2-D polynomials and 2-D Hurwitz-Schur stability. The main advantage of the new stability condition is that it is applicable to the general case of networked systems with multiple, incommensurate delays yet numerically tractable. The characteristic polynomials of networked systems are mapping into 2-D hybrid polynomials, then to test the Hurwitz-Schur stability can. determine the networked systems, examples including system simulations verify the validity of the proposed test algorithms.

The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.

Pass-and-swap queues

Order-independent (OI) queues, introduced by Berezner et al. (Queueing Syst 19(4):345–359, 1995), expanded the family of multi-class queues that are known to have a product-form stationary distribution by allowing for intricate class-dependent service rates. This paper further broadens this family by introducing pass-and-swap (P&S) queues, an extension of OI queues where, upon a service completion, the customer that completes service is not necessarily the one that leaves the system. More precisely, we supplement the OI queue model with an undirected graph on the customer classes, which we call a swapping graph, such that there is an edge between two classes if customers of these classes can be swapped with one another. When a customer completes service, it passes over customers in the remainder of the queue until it finds a customer it can swap positions with, that is, a customer whose class is a neighbor in the graph. In its turn, the customer that is ejected from its position takes the position of the next customer it can be swapped with, and so on. This is repeated until a customer can no longer find another customer to be swapped with; this customer is the one that leaves the queue. After proving that P&S queues have a product-form stationary distribution, we derive a necessary and sufficient stability condition for (open networks of) P&S queues that also applies to OI queues. We then study irreducibility properties of closed networks of P&S queues and derive the corresponding product-form stationary distribution. Lastly, we demonstrate that closed networks of P&S queues can be applied to describe the dynamics of new and existing load-distribution and scheduling protocols in clusters of machines in which jobs have assignment constraints.

Further Results on Performance Guarantees in Adaptive Control of Uncertain Systems With Unmodeled Dynamics

Adaptive control approaches are effective system-theoretical methods for guaranteeing both the stability and the performance of physical systems subject to uncertainties. However, the stability and performance of these approaches can be severely degraded by the presence of unmodeled dynamics. Motivated by this standpoint, the previous work of the authors introduced a model reference adaptive control architecture based on the direct uncertainty minimization method for systems with additive input uncertainties and unmodeled dynamics. In particular, the proposed approach not only guaranteed the closed-loop stability predicated on a sufficient stability condition but also improved the closed-loop performance. The purpose of this paper is to generalize this previous work of the authors. Specifically, a model reference adaptive control architecture is given and it is system-theoretically analyzed for systems with unmodeled dynamics, and both additive input and control effectiveness uncertainties (we refer to Theorems 1 and 2 of this paper). The sufficient stability condition of the resulting architecture relies on linear matrix inequalities and this architecture can be effective in achieving not only stability but also a desired level of closed-loop system performance. Finally, we also provide an illustrative numerical example, which demonstrates the given theoretical results. (This research was supported by the Air Force Research Laboratory Aerospace Systems Directorate under the Universal Technology Corporation Grant 162642-20-25-C1.)

Stability analysis of the high-order nonlinear extended state observers for a class of nonlinear control systems

The nonlinear extended state observer (ESO) is a novel observer for a class of nonlinear control system. However, the non-smooth structure of the nonlinear ESO makes it difficult to measure the stability. In this paper, the stability problem of the nonlinear ESO is considered. The describing function (DF) method is adopted to analyze the stability of high-order nonlinear ESOs. The main result of the paper shows the existence of the self-oscillation and a sufficient stability condition for high-order nonlinear ESOs. Based on the analysis results, we give a simple and fast parameter tuning method for the nonlinear ESO and the active disturbance rejection control (ADRC). Realistic application simulations show the effectiveness of the proposed parameter tuning method.