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Analysis and synthesis of switched linear control systems. (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 \[ \begin{aligned} \delta x(t)&=A_{\sigma}x(t)+B_{\sigma}u(t),\\ y(t)&=C_{\sigma}x(t), \end{aligned} \] 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 \(\mathcal F=\{1,2,\dots ,m\}\), \(\delta\) denotes the derivative operator in continuous time (\(\delta x(t)=(d/dt)x(t)\)) and the shift-forward operator in discrete time (\(\delta x(t)=x(t+1)\)). 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/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B05 Controllability
93D15 Stabilization of systems by feedback
93B12 Variable structure systems
93C65 Discrete event control/observation systems
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