L 2 stability, H ∞ control of switched homogeneous nonlinear systems and their semi‐tensor product of matrices representation

SUMMARY This paper investigates the problems of L 2 stability and H ∞ control of switched homogeneous nonlinear systems. This paper gives that if a switched homogeneous nonlinear system with disturbance is internally homogeneously asymptotically stable, then it has a finite L 2 gain, and if a switched homogeneous nonlinear system with disturbance and controls is homogeneously stabilizable under the zero disturbance condition, its H ∞ control problem is solvable under some mild conditions, and a homogeneous solution is given. Then, via the semi‐tensor product of matrices method, the aforementioned obtained results are transformed to linear‐like forms, and the aforementioned obtained Hamilton–Jacobi–Isaacs inequality is transformed to a linear‐like matrix inequality, which makes it feasible to compute the solutions by computer. Copyright © 2012 John Wiley & Sons, Ltd.