Robust stabilizing compensators for flexible structures with collocated controls

Applied Mathematics and Optimization

Volumn 33, Issue 1, 1996, Pages 35-60

  Balakrishnan, A V ^a  

^a University of California   (United States)

Author keywords

Abstract wave equation; Compensators; Positive real; Resolvent; Robustness; Semigroup; Strong stability

Indexed keywords

ACTUATORS; COMPUTATIONAL COMPLEXITY; CONTINUUM MECHANICS; CONTROL THEORY; FEEDBACK CONTROL; FLEXIBLE STRUCTURES; MATHEMATICAL MODELS; MODEL STRUCTURES; ROBUSTNESS (CONTROL SYSTEMS); SENSORS; SYSTEM STABILITY; TRANSFER FUNCTIONS;

ABSTRACT WAVE EQUATION; COMPENSATORS; EXPONENTIAL STABILITY; KALMAN-YAKUBOVIC LEMMA; POSITIVE REAL; RESOLVENT; SEMIGROUP;

CONTROL SYSTEMS;

EID: 0029755167     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01187961     Document Type: Article

References (16)

1. Arendt, W., and Batty, C. J. K. (1988). Tauberian theorems and stability of one-parameter semigroups. Transactions of the American Mathematical Society, 306:837-852.
2. Balakrishnan, A. V. (1980). Applied Functional Analysis, 2nd edition. Springer-Verlag, New York.
3. Balakrishnan, A. V. (1991). Compensator design for stability enhancement with collocated controllers. IEEE Transactions in Automatic Control, 36:994-1007.
4. Balakrishnan, A. V., and Triggiani, R. (1993). Lack of generation of strongly continuous semigroups by the damped wave operator on H x H (or: the little engine that couldn't). Applications of Mathematics, Letters, 6:33-37.
5. Benhabib, R. J., Iwens, R. P., and Jackson, R. L. (1981). Stability of LSS control systems using positivity concepts. Journal of Guidance and Control, 4:487-494.
6. Doob, J. L. (1954). Stochastic Processes. Wiley, New York.
7. Fattorini, H. (1983). The Cauchy Problem. Addison-Wesley, Reading, MA.
8. Gohberg, I. C., and Krein, M. G. (1969). Introduction to the Theory of Linear Non-Self-Adjoint Operators. American Mathematical Society, Providence, RI.
9. Hille, E. (1962). Analytic Function Theory, Vol. II. Ginn, New York.
10. How, J. P., and Hall, S. R. (1993). Robust controllers for the Middeck active control experiment using Popov controller synthesis. Proceedings of the AIAA Guidance and Control Conference, August 1993, Monterey, California.
11. Joshi, S. (1991). Generalized proportional-plus-derivative compensators for a class of uncertain plants. AIAA Journal of Guidance, Control and Dynamics, 14:677-680.
12. Kalman, R. E. (1963). Lyapunov functions for the problem of lur'e in automatic control. Proceedings of the National Academy of Sciences of the United States of America, 49:201-205.
13. McLaren, M. D., and Slater, G. L. (1987). Robust multivariable control of large space structures using positivity. AIAA Journal of Guidance, Control and Dynamics, 10:393-400.
14. Morse, P. M., and Feshback, H. (1953). Methods of Theoretical Physics. McGraw-Hill, New York.
15. Nagal, R. (ed.) (1980). One-Parameter Semigroups of Positive Operators. Lecture Notes in Mathematics, Vol. 1184. Springer-Verlag, Berlin.
16. Newcomb, R. W. (1966). Linear Multiport Synthesis. McGraw-Hill, New York.