For dynamic systems, it is known that stability (in general) cannot be guaranteed for individually-stabilizing controllers in combination, so the combined system must be analyzed to ensure stability. This paper presents a simple, graphical proof of Lyapunov stability for parallel controllers of SISO, input-affine, autonomous systems. This encompasses a broad range of all linear autonomous systems and many nonlinear, autonomous SISO systems. The proof allows Lyapunov stability theory to be used instead of the more complex and restrictive passivity approach. The paper also explains why it is often desirable to place controllers in parallel.

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