Analytic Solution to Inner-Outer & Spectral Factorization Problems and Its MATLAB Simulation
|School||Shanghai Jiaotong University|
|Course||Control Theory and Control Engineering|
|Keywords||Inside and outside the decomposition Spectral decomposition Zero Zero direction Lyapunov equation|
Inside and outside the decomposition and spectral decomposition problem is an important issue in the field, and its wide range of applications, have played a key role in many important issues. This article first introduced in the first chapter decomposition and spectral decomposition problems inside and outside the three main areas of application, namely: the problem of robust filtering, linear quadratic control problem and H 2 / H ∞ optimal control problem, and describes the In these three areas, both inside and outside decomposition and spectral decomposition method is how to play an important role. The subsequent Chapter II important internal and external decomposition methods in an international context, history and spectral decomposition method, and they each have advantages and disadvantages are compared. As foreshadowing the end of this chapter describes the new internal and external decomposition and spectral decomposition algorithm characteristics and the basic idea, that is \The subsequent algorithm derivation process in order to enable the reader to better understand and appreciate the analysis process as well as the burden of proof process, this paper centrally in the third chapter presents some of the basic concepts in the later chapters will be used directly or penetration which, including the the concept of control theory and mathematical concepts. The core content - a new resolve internal and external decomposition and spectral decomposition algorithm derivation and the proof is presented in Chapter 4. For both types of systems, ie: only a single re-open right half plane zero system and a system of multiple open right half plane zero, respectively, by using complex analysis techniques to obtain analytical equations. In this paper, the new method compared with pure digital computationally simpler and more efficient: the entire calculation process, just to find the open right half plane zero, its zero direction, then calculated according to the procedures . This paper will use the example simulation to illustrate this. This paper presents a new parsing algorithm Another prominent advantage easily combined with mathematical calculation tool software (eg: MATLAB), and the combination algorithm with higher computational efficiency and easier calculation program. Chapter 1 of this article will focus on this point. Not only in strict accordance with the Chapter proposed the preparation of the new algorithm MATLAB program list will be given to cases in MATLAB recalculated, intuitive and vivid proof of the correctness of the program and efficient operator, and three digital 4.3 sex. Finally, the sixth chapter of the full text of the summary of the outlook on future research topics, of which the most important is to make studies of new internal and external decomposition and spectral decomposition algorithm and the practical application of the combination of, should be the role and value of play. Such as: IMC control structure to derive the optimal controller, the new algorithm is applied to where you can get a completely resolve the derivation of the optimal controller. This will become the focus of future work.