## 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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