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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

$\begin{array}{cc}\hfill \delta x\left(t\right)& ={A}_{\sigma }x\left(t\right)+{B}_{\sigma }u\left(t\right),\hfill \\ \hfill y\left(t\right)& ={C}_{\sigma }x\left(t\right),\hfill \end{array}$

where $x\in {ℝ}^{n}$ is the state, $u\in {ℝ}^{p}$ is the control input, $\sigma$ is the piecewise constant switching signal taking values from the finite index set $ℱ=\left\{1,2,\cdots ,m\right\}$, $\delta$ denotes the derivative operator in continuous time ($\delta x\left(t\right)=\left(d/dt\right)x\left(t\right)$) and the shift-forward operator in discrete time ($\delta x\left(t\right)=x\left(t+1\right)$). 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