*(English)*Zbl 1074.93025

Recently, switched control systems have been attracting much attention because the problems are not only academically challenging, but also of practical importance. The paper provides a concise and timely survey on analysis and synthesis of switched linear control systems described by

where $x\in {\mathbb{R}}^{n}$ is the state, $u\in {\mathbb{R}}^{p}$ is the control input, $\sigma $ is the piecewise constant switching signal taking values from the finite index set $\mathcal{F}=\{1,2,\cdots ,m\}$, $\delta $ denotes the derivative operator in continuous time ($\delta x\left(t\right)=(d/dt)x\left(t\right)$) and the shift-forward operator in discrete time ($\delta x\left(t\right)=x(t+1)$). The paper presents the basic concepts and main properties of switched linear control systems in a systematic manner. The fundamental topics include

(i) controllability and observability,

(ii) system structural decomposition,

(iii) feedback controller design for stabilization, and

(iv) optimal control.

The paper includes a useful and rich list of references.

##### MSC:

93C30 | Control systems governed by other functional relations |

93-02 | Research monographs (systems and control) |

93B05 | Controllability |

93D15 | Stabilization of systems by feedback |

93B12 | Variable structure systems |

93C65 | Discrete event systems |