Reduced-order \(H_\infty\) filter with controller design for switched systems. (English) Zbl 1543.93029
Summary: This paper deals with reduced-order \(H_\infty\) filter with controller design for switched systems when the states are not directly observable. A reduced-order \(H_\infty\) filter is firstly used to achieve state estimation for the considered switched system. Then, a controller is designed based on the reduced-order \(H_\infty\) filter’s states and switched system’s outputs. In this way, not only state estimation but also feedback control can be realized at the same time. A sufficient condition is given to achieve exponential stability with a weighted \(H_\infty\) performance for the generalized error system by Lyapunov function method. A co-design method is also shown for the reduced-order \(H_\infty\) filter and controller. Finally, feasibilities of this study are illustrated by a practically classical railway system model and a numerical example.
MSC:
| 93B11 | System structure simplification |
| 93B36 | \(H^\infty\)-control |
| 93E11 | Filtering in stochastic control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
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