$H_\infty $ Control with Transients
- 1 November 1991
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 29 (6) , 1373-1393
- https://doi.org/10.1137/0329070
Abstract
InHo (or uniformly optimal) control problems, it is usually assumed that the system initial conditions are zero. In this paper, an Ho-like control problem that incorporates uncertainty in initial conditions is formulated. This is done by defining a worst-case performance measure. Both finite and infinite horizon problems are considered. Necessary and sufficient conditions are derived for the existence of controllers that yield a closed-loop system for which the above-mentioned performance measure is less than a prespecified value. State-space formulae for the controllers are also presented.Keywords
This publication has 15 references indexed in Scilit:
- A state space approach to H ∞ optimal controlPublished by Springer Nature ,2005
- A Game Theoretic Approach to $\mathcal{H}^\infty $ Control for Time-Varying SystemsSIAM Journal on Control and Optimization, 1992
- $H^\infty $ Control of Linear Time-Varying Systems: A State-Space ApproachSIAM Journal on Control and Optimization, 1991
- State-Space H ∞ Control Theory and the LQG ProblemPublished by Springer Nature ,1991
- Filtering and smoothing in an H/sup infinity / settingIEEE Transactions on Automatic Control, 1991
- A bisection method for computing the H∞ norm of a transfer matrix and related problemsMathematics of Control, Signals, and Systems, 1989
- State-space solutions to standard H/sub 2/ and H/sub infinity / control problemsIEEE Transactions on Automatic Control, 1989
- State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivitySystems & Control Letters, 1988
- A Course in H∞ Control TheoryPublished by Springer Nature ,1987
- An algebraic solution to the spectral factorization problemIEEE Transactions on Automatic Control, 1967