非线性系统第五讲无源性.ppt

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1、Nonlinear Systems Theory,Hu Jiangping,School of Automation Engineering,University of Electronic Science and Technology of China,Topic 5 Passivity,5.1.Memoryless functions,5.2.State model,5.3.Positive real transfer function,5.4.L2 and Lyapunov stability,5.5.Feedback systems:passivity theorems,Topic 5

2、 Passivity,5.1.Memoryless functions,Ohms law,:the conductance,R:the resistance,Topic 5 Passivity,Nonlinear passive resistive elements,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,u,Topic 5 Passivity,5.1.Memoryless functions,5.2.State mod

3、el,5.3.Positive real transfer function,5.4.L2 and Lyapunov stability,5.5.Feedback systems:passivity theorems,Topic 5 Passivity,5.2.State model,Example:The RLC circuit,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5

4、 Passivity,Topic 5 Passivity,Topic 5 Passivity,5.1.Memoryless functions,5.2.State model,5.3.Positive real transfer function,5.4.L2 and Lyapunov stability,5.5.Feedback systems:passivity theorems,5.3.Positive real transfer function,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivit

5、y,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Exercise:Find the conditions to ensure that the transfer function is SPR,1.,2.,3.,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,5.1.Memoryless functions,5.2.State m

6、odel,5.3.Positive real transfer function,5.4.L2 and Lyapunov stability,5.5.Feedback systems:passivity theorems,Topic 5 Passivity,If the system is output strictly passive with,then it is finite-gain L2 stable,Topic 5 Passivity,Example:Consider the p-input-p-output system,Suppose there is a continuous

7、ly differentiable positive semidefinite function V(x)such that,Topic 5 Passivity,If V(x)satisfies,Topic 5 Passivity,5.4.L2 and Lyapunov stability,Topic 5 Passivity,Topic 5 Passivity,V(x)is positive definite,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,5.1.Memoryless functi

8、ons,5.2.State model,5.3.Positive real transfer function,5.4.L2 and Lyapunov stability,5.5.Feedback systems:passivity theorems,Topic 5 Passivity,5.5.Feedback systems:passivity theorems,Topic 5 Passivity,Case I:,Case II:,Topic 5 Passivity,Topic 5 Passivity,Lemma 6.8 The feedback connection of two outp

9、ut strictly passive systems with,is finite-gain L2 stable,Topic 5 Passivity,Theorem 6.2 Suppose each feedback component satisfies the inequality,Then,the closed-loop map from u to y is finite gain L2 stable if,Finite gain L2 stability,Topic 5 Passivity,Topic 5 Passivity,Topic 5 Passivity,?,Topic 5 P

10、assivity,Lyapunov stability,Topic 5 Passivity,both feedback components are output strictly passive and zero-state observable,one component is strictly passive and the other is output strictly passive and zero-state observable.,Topic 5 Passivity,Topic 5 Passivity,we cannot conclude strict passivity or output strict passivity.,Topic 5 Passivity,