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Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions. (English) Zbl 0857.93088

For the system \(\dot x=(A_0+\sum^L_1 \delta_iA_i)x\) the robust stability for \(|\delta_i|<\alpha\) is studied using a parameter dependent Lyapunov function \(V(x)=x^*P (\delta_1,\dots,\delta_L)x\). This is shown to be equivalent to a certain frequency domain inequality. A comparison with the Popov criterion is made. The paper ends with robust stabilizability based on parameter dependent Lyapunov functions.

MSC:

93D30 Lyapunov and storage functions
93D10 Popov-type stability of feedback systems
93B50 Synthesis problems
93D09 Robust stability
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