Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach

Decentralised sliding mode control for a class of nonlinear interconnected systems

In this paper, a decentralised control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems. Both matched uncertainties in the isolated subsystems and mismatched uncertainties associated with the interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed in a decentralised manner by only employing local information. Conditions are determined which enable information on the interconnections to be employed in decentralised controller design to reduce conservatism. The developed results are applied to an automated highway system. Simulation results pertaining to a high-speed following system are presented to demonstrate the effectiveness of the approach

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

Dynamic network model of banking system stability

This paper presents a dynamic model of banking interactions, which uses interbank connections to study the stability of the banking system. The dynamic model extends previous work on network models of the banking system taking inspiration from large scale, complex, interconnected systems studied within the domain of engineering. The banking system is represented as a network where nodes are individual banks and the links between any two banks consist of interbank loans and borrowing. The dynamic structure of the model is represented as a set of differential equations, which, to the best of our knowledge, is an original characteristic of our approach. This dynamic structure not only allows us to analyse systemic risk but also to incorporate an analysis of control mechanisms. Uncertainty is introduced in the system by applying stochastic shocks to the bank deposits, which are assigned as an exogenous signal. The behaviour of the system can be analysed for different initial conditions and parameter sets. This paper shows some preliminary results under different combinations of bank reserve ratios, bank capital sizes and different degrees of bank inter-connectedness. The results show that both reserve ratio and link rate have a positive effect on the stability of the system in the presence of moderate shocks. However, for high values of the shocks, high reserve ratios may have a detrimental effect on the survival of banks. In future work, we will apply strategies from the domain of control engineering to the dynamic model to characterise more formally the stability of the banking network