Online stability validation using sector analysis

Our previous work has explored the use of compositional stabilization techniques for embedded flight control software[9] based on passivity properties of controller components and systems. Zames[21] presented a compositional behavior-bounding technique for evaluating stability of nonlinear systems based on real intervals representing cones (sectors) that bound possible component behaviors. Many innovations in control theory have developed from his insights. We present a novel use of his sector bound theory to validate the stability of embedded control implementations online. The sector analysis can be implemented as a computationally efficient check of stability for different parts of a control design. The advantage of the online application of this technique is that it takes into account software platform effects that impact stability, such as time delays, quantization, and data integrity. We present a brief overview of the sector concept, our compatible control design approach, application of the technique to model-based embedded control software design, an example of its use to find design defects, and insights that may be drawn from our investigation so far. In the present work we only consider software (discrete-time) control of nonlinear continuous-time systems without switching.