Stabilization of multivariable linear time-invariant systems by proportional-plus-derivative state feedback

Kiritsis, Konstadinos H.

doi:10.2478/candc-2023-0032

Abstract

This paper is devoted to the study of the problem of stabilization by proportional-plus-derivative state feedback for multivariable linear time-invariant systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system obtained by proportional-plus-derivative state feedback from the given multivariable linear time-invariant system. A procedure is given for the computation of stabilizing proportional-plus-derivative state feedback. Our approach is based on properties of real and polynomial matrices.

References

ABDELAZIZ, T. H. S. (2015) Pole placement for single input linear system by proportional-derivative state feedback. ASME J. Dynamic Systems, Meas. & Control, 137 (4), 041015-1-041015-10.
Search in Google Scholar Back to article
ABDELAZIZ, T. H. S. and VALASEK, M. (2005) Eigenstructure assignment by proportional-plus-derivative feedback for second – order linear control systems. Kybernetika, 41 (5), 661-676.
Search in Google Scholar Back to article
ABDELAZIZ, T. H. S. (2017) Pole assignment of multivariable systems using proportional-derivative state feedback. International Journal of Systems and Sciences. 48 (33), 2871-2886.
Search in Google Scholar Back to article
ANTSAKLIS, P. J. and MICHEL, A. (2006) Linear Systems. Birkhauser, Boston.
Search in Google Scholar Back to article
CHU, E. K. and DATTA, B. N. (2006) Numerically robust pole assignment for second-order systems. International Journal of Control. 64 (4), 1113-1127.
Search in Google Scholar Back to article
CHU, E. K. (2002) Pole assignment for second-order systems. Mechanical Systems and Signal Processing, 16 (1), 39-59.
Search in Google Scholar Back to article
CHU, D. and MALABRE, M. (2002) Numerically reliable design for proportional and derivative state-feedback decoupling controller. Automatica 38 (1), 2121–2125.
Search in Google Scholar Back to article
DUAN, G. R. and WANG, G. S. (2004) P-D feedback eigenstructure assignment with minimum control e ort in second order systems.In: IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan. 2-4.
Search in Google Scholar Back to article
DUAN, G. R. and WANG, G. S. (2005) Reconfiguring second-order dynamic systems via P-D feedback eigenstructure assignment: A parametric method. International Journal of Control Automation, and Systems. 3 (1), 109-116.
Search in Google Scholar Back to article
DUAN, G. R. and LIU, G. P. (2003) Complete parametric approach for eigen-structure assignment in a class of second order systems. Automatica 38 (3), 725-729.
Search in Google Scholar Back to article
HARALDSDOTTIR, A., KABAMBA, P.T. and ULSOY, A.G. (1990) Control of linear systems by output plus derivative feedback. Journal of Dynamic Systems Measurement and Control 112 (1), 27-34.
Search in Google Scholar Back to article
HENRION, D., SEBEK, M. and KUCERA, V. (2005) Robust pole placement for second-order systems: an LMI approach. Kybernetika 41 (1), 1-14.
Search in Google Scholar Back to article
KALMAN, R. E. (1963) Mathematical description of linear dynamical systems. SIAM Journal of Control and Optimization 1 (2), 152-192.
Search in Google Scholar Back to article
KIRITSIS, K. H. (2022) Pole assignment by proportional-plus-derivative state feedback for multivariable linear time-invariant system. WSEAS Transactions on Systems and Control 17, 262-268.
Search in Google Scholar Back to article
KUCERA, V. (1991) Analysis and Design of Linear Control Systems. Prentice Hall, London.
Search in Google Scholar Back to article
PUGH, A. C. and RATCLIFFE, P. A. (1979) On the zeros and poles of a rational matrix. International Journal of Control 30 (2), 213-226.
Search in Google Scholar Back to article
ROSENBROCK, H. H. (1970) State-space and Multivariable Systems. Nelson, London.
Search in Google Scholar Back to article
ROSENBROCK, H. H. (1973) On the zeros of the system. International Journal of Control 18 (2), 195-207.
Search in Google Scholar Back to article
ROSENBROCK, H. H. (1974) Structural properties of linear dynamical systems. International Journal of Control 20 (2), 191-202.
Search in Google Scholar Back to article
SERAJI, H. and TAROKH, M. (1977) Design of proportional-plus-derivative output feedback for pole assignment. Proceedings IEE 124 (8), 729-732.
Search in Google Scholar Back to article
SERAJI, H. (1980) Pole placement in multivariable systems using proportional plus derivative output feedback. International Journal of Control 31 (1), 195-207.
Search in Google Scholar Back to article
TAROKH, M. and SERAJI, H. (1977) Proportional –plus-multiple derivative output feedback: A new multivariable controller for pole placement. International Journal of Control 25 (2), 293-302.
Search in Google Scholar Back to article
TREDELMAN, H. L., STOORVOGEL, A. A. and HAUTUS, M. (2001) Control Theory for Linear Systems. Springer-Verlag, London.
Search in Google Scholar Back to article
WANG, G. S., QIANG, L. V. and DUAN, G. R. (2006) Eigenstructure assignment in a class of second order systems. Journal of Control Theory and Applications 4 (3), 302-308.
Search in Google Scholar Back to article
WOLOWICH, W. A. (1974) Linear Multivariable Systems. Springer Verlag, Berlin, New York.
Search in Google Scholar Back to article
WONHAM, W. M. (1967) On Pole assignment in multi-input controllable linear systems. IEEE Trans. Automat. Control 12 (6), 660-665.
Search in Google Scholar Back to article

Stabilization of multivariable linear time-invariant systems by proportional-plus-derivative state feedback

Abstract

Paradigm

My account