ہے کوئی سوگوار، تو کوئی خفا لگے
میرا وہ ہمسفر ہے تو دنیا کو کیا لگے
۔پنچھی خزاؤںمیں بھی اسی کا کریں طواف
یعنی کسی درخت کو تیری دعا لگے
آب و ہوا پہ چھانے لگی ہے شگفتگی
موسم بھی تیرے حسن میں اب مبتلا لگے
آنے لگی صدا، کہ مدد چاہیے ہمیں
ہم بھی عظیم لوگ تھے،کوفے سے جا لگے
سہتے ہیں اضطراب مگر توڑتے نہیں
گلشن میں کوئی پھول اگر بے وفا لگے
مر جائے گا مگر نہیں بیچے گا وہ ضمیر
کشمیر! جس وجود کو تیری ہوا لگے
اک عکس اُس میں کھلتے ہی تصویر ہو گیا
گھر میں جو آئنہ مجھے سب سے جدا لگے
E-Commerce in today’s world is playing an important role in global business. A quantitative and quantitative research was conducted with professional members, employees working in organization which are dealing with E-Business or online working via internet and their views gave an empirical and dynamic approach to make business efficient and effective. Connectivity with market to find best manufacture for goods and for manufacture to finds its buyer for their finished goods. Flow of information become faster and gathering of data become easier to make activities of business to get optimal results. Numbers of goods are available complications to finds goods are removed by complimentary goods. Supplies of goods at proper time in order to meet demand by consumer plays win to win game. Improved methods of technology like RFID make work easier and accessible information about goods to management. Manpower in forms of labor is reducing which leads to decrease in the cost of goods. Ordering cost saves time and gives a specified time both producers to make commodity and consumer for delivery of goods. E-Commerce with contrast of components of supply chain in the form of ware house, logistics, number of listing suppliers, number of listing items on one web in the form of website on one platform give dynamic image to businesses in the race of competitive world. Business transactions done with internet not only reduce time but also make documents or records for longer time able to send data from distant parts of the world. Through websites we can get completive price information and other relevant information for goods.
This thesis proposes a framework that provides suboptimal control laws for a class of minimum-phase nonlinear systems. This class includes systems whose state dynamics are an algebraic sum of their linear and nonlinear sub-dynamics. We propose a systematic method of designing a robust and optimal control law which essentially consists of two components a linear and a nonlinear. It is shown that the proposed control scheme achieves stabilization while providing suboptimality for the class of systems under consideration. Furthermore, the framework provides for a mechanism which is suitable for handling tracking and regulation problems for the class of minimum-phase nonlinear systems by using the Internal Model Principle. Astrikingfeatureoftheproposedframeworkistheflexibilityofstartingwithsynthesizing a Linear-Quadratic-Regulator for linear sub-dynamics of the system and then including a nonlinear control component that stabilizes the nonlinear sub-dynamics of the system. The flexibility offered by the proposed framework is applied firstly to a general class of linear parameter-varying and linear time-varying systems. We extend the flexibility obtained for these two systems to the class of minimum-phase nonlinear systems which are decomposable through existence of an appropriate transformation into their linear and nonlinear sub dynamics. Moreover, we also propose a simplified approach to obtain an approximate yet practical solution to the nonlinear optimal control problem by replacing the requirement of solving Hamilton-Jacobi-Bellman equations with that of the Riccati partial differential equations,andthensynthesizingthenonlinearcomponentofthecontrollawtoachieverobust and suboptimal stabilization