Stability Of Large-scale Interconnected Systems Research Articles

Design of robust decentralised large-scale inter-connected control systems via characteristic locus method

The robust stability of large-scale interconnected systems in the presence of block-structured additive perturbations is studied. It is shown that a Gershgorin-like result is applicable for the analysis of such systems. Based on insight derived from such analysis, a conceptual approach based on the characteristic loci technique is proposed for the design of robust decentralised controller for such systems.

Dissipativity-based decentralized control of interconnected nonlinear chemical processes

This paper presents an approach, based on dissipative systems theory, to the analysis and control design of interconnected nonlinear processes. The objective is to design distributed feedback controllers to achieve plant-wide stability. Extensions of classical results on the stability of large-scale interconnected systems lead to input–output dissipativity constraints for each subsystems, encoded as supply rates from input to output interconnecting ports. For each subsystem, a parameterized nonlinear feedback controller is designed using nonlinear dissipative inequalities to ensure that the aforementioned dissipativity constraints are met in closed-loop. One focus of this paper is the design of domination-based nonlinear feedback controllers to meet the above interconnection constraints. This paper also presents new results on the construction of storage functions for control affine systems, as a generalization of physics-based approaches to dissipative systems theory. Control of interconnected chemical reactors with a recycle stream is presented throughout the paper to demonstrate the proposed construction.

Robust Stability Conditions for Large-Scale Interconnected Systems with Structured and Unstructured Uncertainties

The paper is mainly concerned with the problem of decentralized robust stability of large-scale interconnected systems with structured and unstructured uncertainties. A simple method is presented whereby some sufficient conditions are derived so that asymptotic stability of large-scale interconnected systems can be guaranteed in the presence of uncertain perturbations. The method is also extended to large-scale discrete-time systems and the corresponding robust stability conditions are established for uncertain large-scale discrete-time systems. Finally, two numerical examples are given to demonstrate that our robust stability conditions are less conservative than those reported in the control literature.

Stabilization of Large-Scale Interconnected Systems by Decentralized Dynamic Controllers

This paper considers a decentralized stabilization problem for large-scale inter- connected systems. Dynamic controllers for subsystems are designed sequentially using the proper-stable-factorization approach. Sufficient conditions for simultaneous stabilization of the overall system as well as subsystems are obtained. It is also shown that the closed-loop overall system can be further made connectively stable under appropriate minimum phase conditions.

On the Decentralized Stabilization of Large Scale Systems with Time Delays

The problem of decentralized stabilization of large-scale interconnected systems with delays using local feedback controllers is investigated. By employing the aggregation technique based on the Lyapunov vector function, sufficient degree of stability for each isolated subsystem are determined in order to garantee the overall system stability. This sufficient condition presents a more general decentralized stability test.

Comments on ‘ On decentralized feedback stabilization of large-scale interconnected systems ’

A proposition presented by Mahalanabis and Singh, which asserts that, the stability of each aggregated subsystem implies the stability of a large scale system, is shown to be erroneous.

On decentralized feedback stabilization of large-scale interconnected systems

The paper presents a simple approach for designing decentralized state and output feedback controllers for a class of interconnected systems. The method makes use of a simple stability condition for the systems concerned which is derived by making use of simple Liapunov functions. The results are illustrated numerically.

Stability of two-level control schemes subjected to structural perturbations

Abstract The paper deals with the problem of stability of large-scale interconnected systems with a two-level control subjected to structural perturbations. By means of Lyapunov vectors function, sufficient degrees of stability for each isolated subsystem are determined in order that the overall structure remains stable when perturbations occur between the two levels of control. Numerical features are discussed by means of two examples.