A scalable design method for stabilising decentralised controllers for networks of delay-coupled systems

Abstract

Abstract A methodology is proposed to design stabilising fixed-order decentralised controllers for interconnected systems with identical nodal dynamics and identical local controllers. The systems considered are linear time invariant (LTI) multiple-input multiple-output retarded type time-delay systems. The closed-loop systems of local controllers and subsystems (nodes) are modelled by a system of delay differential algebraic equations. The proposed approach combines the non-conservative direct optimisation approach towards stabilisation of delay systems with a decoupling transformation. The latter reduces the overall design problem to a robust/simultaneous controller design problem for one parameterised subsystem, where the allowable values of the parameter correspond to eigenvalues of the adjacency matrix of the network graph. By treating the eigenvalues as perturbations, contained in specific intervals or regions in the complex plane determined by the topology of the network, and by optimising the corresponding pseudospectral abscissa using a novel structure exploiting algorithm, we can ensure that the achieved stability property, and the computational complexity of the controller design, are independent of the number of subsystems. A numerical example is presented to validate the proposed approach in MATLAB software.