Abstract
In this paper, we investigate a discontinuous state feedback control law for a symmetric affine system with two-generators, whose controllability Lie algebra is essentially different from conventional chained(single-generator) structures. At first, we provide a topological principle to design a discontinuous surface to get rid of the nonexistence of continuous stabilizing feedback, with a pair of illustrative examples of single-generator case. Based on this concept and nonlinear controllability analysis, we propose a discontinuous control strategy for a 2-input 5-state two-generator system.
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