State Estimator Design: Addressing General Delay Structures With Dissipative Constraints

Dissipative estimator (observer) design for continuous time-delay systems poses a significant challenge when multiple pointwise and general distributed delays (DDs) are present. We propose an effective solution to this semiopen problem using the Krasovski functional (KF) framework in conjunction with a quadratic supply rate function, where both the plant and the estimator can accommodate a finite but unlimited number of pointwise and general DDs with square-integrable kernels. A key contribution is the introduction of a control concept called Kronecker–Seuret decomposition (KSD) for matrix-valued functions, which allows for the factorizations or approximations of any DD integral kernel without introducing conservatism. Moreover, using KSD facilitates the construction of complete-type KFs with integral kernels that can contain any number of weakly differentiable and linearly independent functions. Our proposed solution is formulated as sequential convex semidefinite programming (SDP) problems and is set out in two theorems along with an offline iterative algorithm, which eliminates the need for nonlinear numerical solvers. We show the effectiveness of our method using two challenging numerical experiments, including a system stabilized by a nonsmooth controller.