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H_{\infty } Control of Switched Nonlinear Systems in p -Normal Form Using Multiple Lyapunov Functions

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2 Author(s)
Lijun Long ; State Key Lab. of Synthetical Autom. for Process Ind., Northeastern Univ., Shenyang, China ; Jun Zhao

The problem of H control of switched nonlinear systems in p-normal form is investigated in this technical note where the solvability of the H control problem for individual subsystems is unnecessary. Using the generalized multiple Lyapunov functions method and the adding a power integrator technique, we design a switching law and construct continuous state feedback controllers of subsystems explicitly by a recursive design algorithm to produce global asymptotical stability and a prescribed H performance level. Multiple Lyapunov functions are exploited to reduce the conservativeness caused by adoption of a common Lyapunov function for all subsystems, which is usually required when applying the backstepping-like recursive design scheme. An example is provided to demonstrate the effectiveness of the proposed design method.

Published in:

Automatic Control, IEEE Transactions on  (Volume:57 ,  Issue: 5 )