Decomposition-based Control for Switched Non-linear Systems with Vector $L_{2}$-gain

In this paper, we investigate the vector
$L_{2}$
-gain property of switched nonlinear systems. If a switched system does not have the vector
$L_{2}$
-gain property, we decompose the vector of each subsystem and design the counter term of each subsystem to make the system have the vector
$L_{2}$
-gain property with the same storage functions of the decomposition systems. In addition, for interconnected systems, a small-gain theorem can be obtained for switched systems by the decomposition of the vectors of systems and the design of the counter terms. Finally, an example is provided to illustrate the effectiveness of the main results.