TABLE OF CONTENTS G P Liu
Abstract. This chapter is concerned with three different multi-objective control schemes. These are, respectively, PID control, critical control and eigenstructure assignment. In each case the design problem is formulated in accordance with the principle of inequalities. This is a multi-objective design rule where each design specification is expressed as an inequality. In the PID control problem, a set of frequency-domain performance requirements, such as gain margin, phase margin, crossover frequency and steady-state error are used to construct inequalities. In the critical control problem, the issue of robustness of multivariable critical systems with external and internal uncertainties is addressed. The design inequalities are based on the output performance in the time domain and the robust performance in the frequency domain. The eigenstructure assignment problem considers robustness in multivariable control systems. The performance functions are individual eigen-value sensitivity functions and the system robustness functions. Based on those performance functions above, the performance criteria for each multi-objective scheme are expressed by a set of inequalities. Some examples demonstrate the operation of the three multi-objective control schemes.
Most control design techniques have only paid attention to optimal solutions for one special performance index, e.g., 
?-norm on a closed-loop system transfer function, the eigenvalue sensitivity function or the linear quadratic index. However, many practical control systems are required to have the ability to satisfy simultaneously different and often conflicting performance objectives as best as possible, for instance, closed-loop stability, low feedback gains and insensitivity to model parameter...
