Preface

Applications of many mathematical modeling lead us to study the qualitative behaviors, including the controllability/stability of the systems. It is one of the most sought interdisciplinary areas of research and arises in the very first technological discoveries of the Industrial Revolution and modern technological applications. Control theory is an important discipline. It emerged in portfolio diversification strategy for the selected stocks and applications in stability analysis, supply chain dynamics, TCP strategic planning, electrical plant distribution systems, and the stabilization of airplanes.

In this collection of chapters in *Control Systems in Engineering and Optimization Techniques*, we have selected various multi-disciplinary research fields that fall within the ambit of Control Theory and applications. The reader will be given insights on these varieties of topics ranging from financial markets, supply chain dynamics, test case prioritization, static output feedback and applications, experimental study of electric drives, and stability issues in fractional differential systems.

In chapter 1, the best portfolio diversification strategy for the selected stocks from the Tokyo Stock Exchange had been examined using the Markowitz mean value method during different subperiods of time, which revealed several interesting insights. The naïve diversification strategy is used to serve as a comparison for the approach used. Performance-wise the optimal portfolio dominated the naïve strategy throughout the subperiods tested. The stability of fractional differential equations (FDEs) has shown wide applications in various sciences and engineering fields. Chapter 2 deals with the problem of finite-time stability of fractional higher-order stochastic delay systems. The chapter provides compelling ideas about the strength of stochastic fractional stability. Using a solution representation given by using sine-cosine functions for various delay intervals, various existence and uniqueness results are proved through the fixed point theorem. Further, finite-time stability criteria were demonstrated using a fractional Gronwall-Bellman inequality lemma.

Supply chain dynamics essentially deal with the dynamic behavior and temporal variation of the inventories and flows in the system over time when subjected to demand disturbances. In chapter 3, the discrete-time control supply chains problem is studied. Direct operator methods were used instead of the conventional block diagrams and the transfer function theory. The disturbance induced by demand deviation from the planned/anticipated levels was considered by considering the inventory level. Testing software or application is a fundamental part of SDLC. In chapter 4 a novel approach to Test Case Prioritization (TCP) and Strategies are developed and presented.

In chapter 5, an explicit free parametrization is presented for all the stabilizing static-state-feedbacks for continuous-time LTI systems. The parametrizations are utilized to derive optimal control results, pole placement, and exact pole assignment problems. Chapter 6 deals with the results of experiments in which the modes of parrying step loads are represented by the maximum possible recorded

signals-frequency and amplitude of the stator voltage generated by various algorithms, the frequency and amplitude of the rotor current, the natural slip, and the rotational speed of the motor rotor. This made it possible to assess the effectiveness of interpreting asynchronous electric drives and methods of their regulation as objectively as possible. Over the past 25-30 years, numerous articles on this topic have not provided such results.

The book can be used as a reference book for several interdisciplinary research areas. We express our sincere thanks to all the contributors, managing editors, and typesetters.

#### **P. Balasubramaniam** Professor,

Department of Mathematics, Gandhigram Rural Institute, Gandhigram, Tamil Nadu, India

#### **Dr. Sathiyaraj Thambiayya**

Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur, Malaysia

#### **Kuru Ratnavelu**

Professor, Institute of Computer Science and Digital Innovation, UCSI University, Kula Lumpur, Malaysia

#### **JinRong Wang**

Department of Mathematics, Guizhou University, Guiyang, China Section 1
