الفهرس 
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Abstract
In the last decade, non-linear semi-de nite programming problem (NSDP) have
attracted the attention of many authors in the optimization community. For
instance, Jarre [11] introduced an interior point method for non-convex semide
nite programs. Leibfritz and Mostafa [14] proposed an interior-point trustregion
method for a special class of NSDP problems resulting from the continuoustime
static output feedback (SOF) problem. Kocvara and stingl [12] considered
an augmented Lagrangian method for a similar NSDP problem. Sun et al. [30]
investigated the rate of convergence of the augmented Lagrangian approach for
NSDP. Correa and Ramirez [5] proposed a sequential semi-de nite programming
method for non-linear semi-de nite programming problems. Yamashita and Yabe
[34] studied local and super-linear convergence of a primal-dual interior point
method. Mostafa et al. [25] introduced an SQP method globalized using line
search for solving certain NSDP problem originating from discrete-time output
feedback control systems. He introduced an augmented Lagrangian SQP method
for two NSDP originating from such systems. Recently, non-linear optimization
techniques have been employed by several researchers to solve NSDPs arising in
optimal control (see for example, [21], [25]).
Feedback and control is a central feature of life. The process of feedback governs
how we grow, respond to stress and challenge, and regulate factors such as
body temperature, blood pressure and cholesterol level. The mechanisms operate
at every level, from the interaction of proteins in cells to the interaction of organisms
in complex ecologies. Feedback and control are almost everywhere. One
can virtually link the powerful word ”control” to almost anything, such as ”diet
control” ,” nancial control”, ”pest control”, ”motor control”, ”robot control”, etc. One can also say that ”power is nothing without control,” which is believed to be correct in both social and technological contexts. Feedback is an intuitive means for control. For example, when you feel cold (sensing), you add one more layer
of cloth (decision and then control action) to keep yourself warm and comfortable (objective). This is biological feedback due to a change in the environment. The
CHAPTER 1. INTRODUCTION 4
early development of automatic control devices can be traced back to the ancient
water clock in Alexandria, Egypt, or to the ancient compass vehicle developed
about 2,000 years ago during the Han Dynasty in China. The
ying ball governor
invented by James Watt in 1788 is regarded as the rst widely used automatic
feedback control system. Theoretical research on control systems was initiated by
the study of stability problems involving di erential equations pioneered by the
work of Maxwell in 1868, Routh in 1874, and Hurwitz in 1895. Control strategy
design problems were rst proposed by Minorsky in 1922. Robust control is a
very attractive new area in control systems design. Modern robust control investigations
were started by Zames in 1981, where optimal control problems were
formulated as the minimization of norms in Hardy spaces. The state space solution
to such problems by Doyle et al. in 1989 is a signi cant computational
contribution. Most feedback system analysis and design tasks can be solved easily
using a computer. Therefore, suitable computer software is essential for control
system investigations. Control systems can be broadly broken up into two major
categories: open loop control and closed loop control. Systems in which the output
quantity has no e ect upon the process input quantity are called open-loop control
systems. On the other hand, closed-loop control systems are those in which the
output has an e ect upon the process input quantity in such a manner that the
desired output value is maintained (see e.g., [8]).
The design of an optimal output feedback controller that meets a desirable performance
criterion is an important non-linear and non-convex problem in optimal
control theory (see e.g., [22], [20]). Over the last two decades, several problems in
system and control theory were reduced to some special class of non-linear semide
nite programs. Although the NSDP formulations of control systems were made
popular in the mid 1990s, computational methods for solving general non-convex
NSDPs were not yet developed.
The static output feedback problem is one of the most important open problems
in optimal control theory (see [2] and [3]). The optimal SOF control problem was
solved for the discrete-time case using unconstrained optimization techniques (see<br.