Eigenvalue optimisation-based centralised and decentralised stabilisation of time-delay systems

Both centralised and decentralised stabilisation of multi-input multi-output linear time-invariant (LTI) systems with discrete time-delays are considered. No restriction has been made on the number and type of the time-delays. The main objective is to design LTI finite-dimensional static/dynamic stabilising centralised/decentralised output feedback controllers. For this, the decentralised pole assignment algorithm developed for decentralised stabilisation of finite-dimensional systems is extended to the time-delay case. In this approach, decentralised controllers are designed sequentially, where a centralised design approach is used in each step. As the centralised design approach, the eigenvalue optimisation-based stabilisation method is utilised. Regarding the nonconvexity of the optimisation problem, an initialisation procedure, which determines the minimum possible dimension of the stabilising controller and the initial controller parameters, is developed. As a particular case of dynamic output feedback, the decentralised proportional-integral control is also considered. The proposed controller design methods are verified through numerical and practical examples.