Stability Analysis and Synthesis of Linear Systems with Time-Varying Delays
|Course||Operational Research and Cybernetics|
|Keywords||Delay systems H ∞ control Stability Analysis Second method of Lyapunov Linear matrix inequality (LMI)|
Delay phenomenon widely exists in all kinds of engineering and social systems , delay systems can be closer to the physical reality . With the development of industrial technology , just the system has been unable to meet actual work requirements analysis , and we hope that through the design of the controller makes the system performance to meet certain expectations , such as stability , tracking a parameter signal . Ten years based on the requirements for the analysis and synthesis of delay systems has become a hot issue of control theory research . This paper linear varying delay systems based on Lyapunov stability theory , the use of LMI linear matrix inequalities theory of linear variable delay switched system stability problems , and at the same time to explore the types of Linear Variable Delays system design issues , mainly including : the linear varying delay systems Hoo output tracking controller design problem and linear variable Delay discrete systems Robust Hoo filter problem . The first chapter introduces the research significance of the linear varying delay systems and some of the current research status and the paper work ; second chapter describes some basic concepts and theory of this thesis will be used to ; first three chapters study the design issues of a of linear Varying Delay System Hoo output tracking controller , a new controller design method based on Lyapunov second method , making the role of the controller to meet H ∞ output tracking performance ; Chapter linear variable Delay discrete system robust Hoo filter design problem , using a similar method , based on linear matrix inequalities ( LMI ) stability criterion of the new system and robust H ∞ filter design methods ; Chapter study linear variable Delay switching system stability problem by introducing a less conservative inequality , a new system is stable and sufficient condition . At the end of each chapter are numerical examples to prove the validity of the conclusions , the feasibility . And in the final summary of the full text of future vision and direction .