杭州电子科技大学现代控制理论基础课件第三章 可控性和可观性（2）.ppt

Modern Control Theory Lecture 8 Modern Control Theory Letures Notes Coryrighr@Xiaodong zhao 3.3 Duality principle 3.3.1 dual relation of linear system 3.3.2 Dual relation of controllability observability Proof: 3.4 Controllable Observable Canonical Realization Controllable Canonical Realization Theorem 3-11 The following system is called controllable canonical realization and it is controllable. Proof: Theorem 3-12 Let LTI system be If the system is controllable, there exists non-singular transformation and translate the above system to controllable canonical realization. Proof: Assume Example 3-9 2. Observable Canonical Realization Theorem 3-13 The following system is called observable canonical realization and it is observable. Proof: Theorem 3-14 Let LTI system be If the system is observable, there exists non-singular transformation and translate the above system to observable canonical realization. Proof: Assume 3.4.2 Controllable Observable Canonical Realization of MIMO system If the system is controllable, there exists non-singular transformation and translate the above system to controllable canonical realization If the system is observable, there exists non-singular transformation and translate the above system to observable canonical realization. 3.5 Controllablity Observablity of LDTI System 3.5.1 Controllablity Definition: For given initial state if there exists and input signal such that the system is said to be controllable. Theorem 3-15: The above system is controllable iff Proof: Example 3-11 Example 3-12 3.6 structure decomposition 3.6.1 controllable structure decomposition Theorem 3-17 For non-controllable LTI system if then there exists non-singular linear transform such that The system is decom