L2 stability,H∞ control of switched homogeneous nonlinear systems and their semi‐tensor product of matrices representation |
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Authors: | Kuize Zhang |
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Affiliation: | College of Automation, Harbin Engineering University, , Harbin, 150001 China |
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Abstract: | This paper investigates the problems of L2 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 L2 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. |
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Keywords: | switched homogeneous nonlinear system L2 stability H∞ control semi‐tensor product (STP) of matrices linear‐like matrix inequality |
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