This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disad-vantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t0). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.

1.
Anderson
B. D. O.
, and
Moore
J. B.
,
1968
, “
Extensions of Quadratic Minimization Theory, II. Infinite Time Results
,”
Int. J. Control
, Vol.
7
, pp.
473
480
.
2.
Arvanitis
K. G.
, and
Paraskevopoulos
P. N.
,
1992
, “
Uniform Exact Model Matching for a Class of Linear Time-Varying Analytic Systems
,”
Systems and Control Letters
, Vol.
19
, pp.
312
323
.
3.
Callier, F., and Desoer, C. A., 1992, Linear System Theory, Springer-Verlag, Hong Kong.
4.
Chen, C. T., 1984, Linear System Theory and Design, Holt, Rinehart and Winston, New York.
5.
Kalman, R. E., 1964, “When Is a Linear Control System Optimal,” ASME Journal of Basic Engineering, pp. 51–60.
6.
Kalman, R. E., and Bucy, R. S., 1961, “New Results in Linear Filtering and Prediction Theory,” ASME Journal of Basic Engineering, pp. 95–108.
7.
Kwakernaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley, New York.
8.
Rugh, W. J., 1993, Linear System Theory, Prentice-Hall, Englewood Cliffs, NJ.
9.
Valasek, M., and Olgac, N., 1993, “Generalization of Ackermann’s Formula for Linear MIMO Time Invariant and Time Varying Systems,” Proceedings of Conference on Decision and Control, pp. 827–831.
10.
Wolovich
W. A.
,
1968
, “
On the Stabilization of Controllable Systems
,”
IEEE Trans. Automat. Contr.
, Vol.
13
, pp.
569
572
.
11.
Wonham
W. M.
,
1968
, “
On a Matrix Riccati Equation of Stochastic Control
,”
SIAM J. Control
, Vol.
6
, pp.
681
697
.
This content is only available via PDF.
You do not currently have access to this content.