## Quadratic stabilization of a class of switched nonlinear systems via single Lyapunov function.(English)Zbl 1179.93152

Summary: This paper is concerned with the problem of globally quadratic stabilization for a class of switched cascade systems. The system under consideration is composed of two subsystems: a linear switched part and a nonlinear part, which are also switched systems. The feedback control law and the switching law are designed respectively when the first part is stabilized under some switching law and when both parts can be stabilized under some switching laws. We construct the single Lyapunov functions and design the switching laws based on the structure characteristics of the switched system. Also, the designed switching laws are of hysteresis switching form in order to avoid sliding models.

### MSC:

 93D21 Adaptive or robust stabilization 93B52 Feedback control 93C15 Control/observation systems governed by ordinary differential equations 93B12 Variable structure systems
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### References:

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