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This paper derives for non-linear, time-varying and feedback linearizablesystems simple controller designs to achieve specified state-and timedependentcomplex convergence rates. This approach can be regarded as a generalgain-scheduling technique with global exponential stability guarantee. Typicalapplications include the transonic control of an aircraft with strongly Mach ortime-dependent eigenvalues or the state-dependent complex eigenvalue placementof the inverted pendulum. As a generalization of the LTI Luenberger observer adual observer design technique is derived for a broad set of non-linear andtime-varying systems, where so far straightforward observer techniques were notknown. The resulting observer design is illustrated for non-linear chemicalplants, the Van-der-Pol oscillator, the discrete logarithmic map seriesprediction and the lighthouse navigation problem. These results [23] allow oneto shape globally the state- and time-dependent convergence behaviour ideallysuited to the non-linear or time-varying system. The technique can also be usedto provide analytic robustness guarantees against modelling uncertainties. Thederivations are based on non-linear contraction theory [18], a comparativelyrecent dynamic system analysis tool whose results will be reviewed andextended.

Shaping state and time-dependent convergence rates in non-linear control and observer design