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A Geometric Approach to Large-signal Stability of Switching Converters under Sliding Mode Control and Synergetic Control

The objective is to study the large-signal stability of switching converters operating in sliding mode or under synergetic control. Under both control approaches, the system state reaches a desired control manifold and then stays on that manifold at all times. The question of stability on the control manifold is examined, i.e., whether the system converges to the desired steady-state point. The proposed geometric method allows the determination of the direction of evolution at any point on a control manifold, therefore providing large-signal stability information. Stability conditions with a clear geometric interpretation can be established for any point on a control manifold. In particular, if the method is applied to the steady-state operating point, it yields stability conditions that exactly match conditions obtained from a small-signal linearized analysis. This validates and demonstrates the power of the proposed approach. The method is fairly general and it can be applied to any second-order converter. The paper discusses the cases of buck, boost and buck-boost converters under resistive load and under constant power load, a case of particular interest in multi-converter systems