Title :
A rigorous approach to H∞ control with transients
Author :
Lu, Wayne W. ; Balas, Gary J. ; Lee, E. Bruce
Author_Institution :
Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN, USA
Abstract :
This paper presents a variational approach to H∞ control with transients in the state feedback case. The problem was formulated in Khargonekar et al. (1991). The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are also proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant plant (LTV) on a finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on an infinite horizon. By this approach, it can be directly concluded that only sub-optimal H∞ state feedback control can be achieved from an input/output point of view and that the performance measure γ(μ 1/2 used in this paper) is a strict upper bound
Keywords :
H∞ control; Riccati equations; linear systems; matrix algebra; multidimensional systems; nonlinear differential equations; state feedback; time-varying systems; transients; variational techniques; H∞ control; finite horizon; indefinite Riccati equations; infinite horizon; linear controller; linear time-invariant plant; linear time-variant plant; necessary and sufficient conditions; performance measure; rigorous approach; solution existence; solution uniqueness; state feedback; strict upper bound; transients; variational approach; Boundary conditions; Differential equations; Eigenvalues and eigenfunctions; Infinite horizon; Integral equations; Partial differential equations; Riccati equations; Steady-state;
Conference_Titel :
Decision and Control, 1996., Proceedings of the 35th IEEE Conference on
Conference_Location :
Kobe
Print_ISBN :
0-7803-3590-2
DOI :
10.1109/CDC.1996.573133
