Details

Autor(en) / Beteiligte

• GLIZER, V. Y

Titel

Asymptotic analysis and solution of a finite-horizon H∞ control problem for singularly-perturbed linear systems with small state delay

Ist Teil von

• Journal of optimization theory and applications, 2003-05, Vol.117 (2), p.295-325

Ort / Verlag

New York, NY: Springer

Erscheinungsjahr

2003

Link zum Volltext

Quelle

SpringerLink Journals

Beschreibungen/Notizen

• A finite-horizon H∞ state-feedback control problem for singularly-perturbed linear time-dependent systems with a small state delay is considered. Two approaches to the asymptotic analysis and solution of this problem are proposed. In the first approach, an asymptotic solution of the singularly-perturbed system of functional-differential equations of Riccati type, associated with the original H∞ problem by the sufficient conditions of the existence of its solution, is constructed. Based on this asymptotic solution, conditions for the existence of a solution of the original H∞ problem, independent of the small parameter of singular perturbations, are derived. A simplified controller with parameter-independent gain matrices, solving the original H∞ problem for all sufficiently small values of this parameter, is obtained. In the second approach, the original H∞ problem is decomposed into two lower-dimensional parameter-independent H∞ subproblems, the reduced-order (slow) and the boundary-layer (fast) subproblems; controllers solving these subproblems are constructed. Based on these controllers, a composite controller is derived, which solves the original H∞ problem for all sufficiently small values of the singular perturbation parameter. An illustrative example is presented.