Stability And Time Optimal Control Of Hereditary Systems

Stability and Time-Optimal Control of Hereditary Systems is the mathematical foundation and theory required for studying in depth the stability and optimal control of systems whose history is taken into account. In this edition, the economic application is enlarged, and explored in some depth. The application holds out the hope that full employment and high income growth will be compatible with low prices and low inflation, provided that the control matrix has full rank, i.e., the existing controls are fully effectively used. The book concludes with a new appendix containing complete programs, data, graphs and quantitative results for the US economy.

Stability and Time-Optimal Control of Hereditary Systems is the mathematical foundation and theory required for studying in depth the stability and optimal control of systems whose history is taken into account. In this edition, the economic application is enlarged, and explored in some depth. The application holds out the hope that full employment and high income growth will be compatible with low prices and low inflation, provided that the control matrix has full rank, i.e., the existing controls are fully effectively used. The book concludes with a new appendix containing complete programs, data, graphs and quantitative results for the US economy.

Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and

This monograph derives from familiar economic principles the dynamics of national income, the interest rate, employment, the value of capital stock, prices, and the cumulative balance of payments. This is a Volterra neutral integrodifferential game of pursuit. The quarry control is government intervention in the form of taxation, control of money supply, tariffs, foreign credit, interest equalization tax, preferential trade agreements (which reduce trade barriers and enhance trade flows between nations), transportation and distance between trading partners. The pursuer controls include wages and productivity. The book provides conditions for controllability and then deduces how big government intervention (compared with private firms' contributions) should be to ensure the possibility of growth.The reader is assumed to be familiar with advanced calculus and to have a working knowledge of ordinary differential equations. The required theory of hereditary systems can be obtained from the book itself.

This monograph, a sequel to the author's highly successfull A Mathematical Treatment of Economic Cooperation and Competition Among Nations: With Nigeria, USA, UK, China and Middle East Examples (Academic Press, 2005), extends the study to all member states of the United Nations. It derives the equations of the key economic variables of gross domestic product, interest rate, employment value of capital stock prices (inflation) and cumulative balance of payment. The derivation is based on the differential market principle of supply and demand and on the rational expectation principle. The models are validated using economic time series of each country and MATLAB programs. The emerging dynamics is a differential game of pursuit which is converted to a hereditary control system for a single nation. Following the same method we derive the full hereditary economic model of all members of the United Nations joined together by external trade, investment capital flow consumption employment and governments' economic intervention all mirrored by interacting gross domestic products. The system is validated with IMF and World Bank data.Studies are made on how to arrest economic recession and depression and promote economic growth and prosperity. Diffusion of wealth is also touched upon. Policies regarding economic stimulus, how to dam the decay of capital flow, as well as conditions to promote full employment are discussed. Examination is made to test for the global systems controllability the possibility of steering any current bad economic state to a state of growth of its GDP, low interest rate, full employment, good value of capital stock, low inflation and a positive value of the cumulative balance of payments. The book prescribes verifiable broad policies for all nations together to promote prosperity, diffusion of wealth and longevity. The book comes with full programs, output and identified equations which can be downloaded from the publishers' website. Detailed information is available inside the book.The book is a most valuable source of reference for world leaders, central bank directors, graduates and academic researchers in applied mathematics and applied economics concerned with the current problems and growth of the global economy.

This monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient characterizations are proposed. This monograph addresses general delay problems and offers solutions in some cases. In other cases, approximations of the stability regions can be proposed. The interpretation of delays as uncertainty allows the authors to use the advances in robust control and robust convex optimization to solve or to approximate the solutions of the corresponding problems.