# Optimal disturbance rejection and performance robustness in linear systems

## Abstract

In this chapter a method is proposed for the optimal design of regulators and observers from the disturbance rejection and robust performance points of view. For a given set of system parameters, we obtain a measure of the disturbance rejection capacity of the system or observer. Optimization routines need to be employed to select control or observer gains which maximize the disturbance rejection capacity. The general case of time-varying linear systems is considered and time-domain techniques are employed. Also the problem of achieving maximum performance as well as required robustness in the presence of parameter uncertainties is considered. An expression is derived for the variation of performance with parameter changes. The methodology has connections to the *H*_{∞} methods in the case of time-invariant systems. An application to an aircraft wing leveler system is given to illustrate the methodology.

## Keywords

Transition Matrix Integral Inequality Disturbance Rejection Optimization Routine Sideslip Angle## Preview

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## References

- [1]M. B. Subrahmanyam, On applications of control theory to integral inequalities,
*SIAM J. Contr. Optimiz.***19**, 1981, pp. 479–489.Google Scholar - [2]—M. B. Subrahmanyam, On integral inequalities associated with a linear operator equation,
*Proc. Amer. Math. Soc.***92**, 1984, pp. 342–346.Google Scholar - [3]—M. B. Subrahmanyam, Necessary conditions for minimum in problems with nonstandard cost functionals,
*J. Math. Anal. Appl.***60**, 1977, pp. 601–616.Google Scholar - [4]—M. B. Subrahmanyam, On applications of control theory to integral inequalities,
*J. Math. Anal. Appl.***77**, 1980, pp. 47–59.Google Scholar - [5]—M. B. Subrahmanyam, A control problem with application to integral inequalities,
*J. Math. Anal. Appl.***81**, 1981, pp. 346–355.Google Scholar - [6]—M. B. Subrahmanyam, An extremal problem for convolution inequalities,
*J. Math. Anal. Appl.***87**, 1982, pp. 509–516.Google Scholar - [7]B. A. Francis and J. C. Doyle, Linear control theory with an
*H*_{∞}optimality criterion,*SIAM J. Contr. Optimiz.***25**, 1987, pp. 815–844.Google Scholar - [8]B. A. Francis, “A Course in
*H*_{∞}Optimal Control Theory,” Lecture Notes in Control and Information Sciences, Vol. 88, Berlin, Springer-Verlag, New York, 1987.Google Scholar - [9]E.B. Lee and L. Markus, “Foundations of Optimal Control Theory,” Wiley, New York, 1967.Google Scholar
- [10]D. R. Downing and J. R. Broussard, Digital Flight Control System Analysis and Design,” Short Course Notes, University of Kansas, Lawrence, KS.Google Scholar
- [11]G. H. Golub and C.F. Van Loan, “Matrix Computations,” Johns Hopkins, Baltimore, MD, 1983, p. 384.Google Scholar
- [12]J. L. Kuester and J. H. Mize, “Optimization Techniques with Fortran,” McGraw-Hill, New York, 1973.Google Scholar