Robust Control of General Linear Delay Systems under Dissipativity: Part I -- A KSD-based Framework
This work addresses control design challenges for linear delay systems, which is incremental as it builds on existing KF approaches with a novel decomposition method.
The paper tackles the problem of designing memoryless dissipative full-state feedback for general linear delay systems with multiple pointwise and distributed delays by introducing a framework based on the Kronecker-Seuret Decomposition (KSD) to handle infinite-dimensional delays without conservatism, resulting in theorems and an iterative algorithm for controller gain computation, with effectiveness demonstrated through a numerical example.
This paper introduces an effective framework for designing memoryless dissipative full-state feedback for general linear delay systems via the KrasovskiÄ functional (KF) approach, where an arbitrary finite number of pointwise and general distributed delays (DDs) exists in the state, input and output. To handle the infinite dimensionality of DDs, we employ the Kronecker-Seuret Decomposition (KSD) which we recently proposed for analyzing matrix-valued functions in the context of delay systems. The KSD enables factorization or least-squares approximation of any number of $\fL^2$ DD kernels from any number of DDs without introducing conservatism. This also facilitates the construction of a complete-type KF with flexible integral kernels by means of a novel integral inequality derived from the least-squares principle. Our solution includes two theorems and an iterative algorithm to compute controller gains without relying on nonlinear solvers. A numerical example is tested to show the effectiveness of the proposed approach.