Estimation and Feedback in Linear Time-Varying Systems: A Deterministic Theory
- 1 February 1975
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control
- Vol. 13 (2), 304-326
- https://doi.org/10.1137/0313018
Abstract
The problems of (i) state-variable feedback, (ii) deterministic state estimation, and (iii) state estimation and feedback are considered for a finite-dimensional linear time-varying system. The following are the questions; they can be regarded as natural and logical extensions to a time-varying case of the pole assignment problem [2]–[6] for a time-invariant system. (i) What is the relation between controllability and reachability of an open loop system and the possibility of constructing a linear state-variable feedback law which realizes the prescribed stability and instability degrees of the closed loop system? (ii) What is the relation between observability and reconstructibility of the system to be estimated and the possibility of constructing a linear state estimator which realizes the prescribed stability and instability degrees of the estimate error? (iii) What is the relation between controllability, reachability, observability and reconstructibility of an open loop system and the possibility of constructing a linear feedback compensator composed of a state estimator and an amplifier which realizes the prescribed stability and instability degrees of the closed loop system? Here, the stability and instability degrees mean the indices of exponential functions which bound the (zero-input) response from above and below respectively. This paper gives some principal answers to the questions.Keywords
This publication has 11 references indexed in Scilit:
- Stabilization of Linear SystemsSIAM Journal on Control, 1972
- Linear Optimal ControlJournal of Dynamic Systems, Measurement, and Control, 1971
- New Results in Linear System StabilitySIAM Journal on Control, 1969
- A deterministic theory of estimation and controlIEEE Transactions on Automatic Control, 1969
- A theory of modal controlInformation and Control, 1968
- On the stabilization of controllable systemsIEEE Transactions on Automatic Control, 1968
- Controllability, Observability and Stability of Linear SystemsSIAM Journal on Control, 1968
- On pole assignment in multi-input controllable linear systemsIEEE Transactions on Automatic Control, 1967
- Contributions to linear system theoryInternational Journal of Engineering Science, 1965
- Poles, zeros, and feedback: State space interpretationIEEE Transactions on Automatic Control, 1965