Adaptive stabilization using a nonlinear time-varying controller |
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Authors: | Miller D.E. |
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Affiliation: | Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont.; |
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Abstract: | Byrnes et al. (1986) showed that there is no smooth, finite-dimensional, nonlinear time-invariant (NLTI) controller which asymptotically stabilizes every finite-dimensional, stabilizable and detectable, linear time-invariant (LTI) plant (with a fixed number of inputs and outputs). Here we construct a finite-dimensional nonlinear time-varying (NLTV) controller which does exactly that; we treat both the discrete-time and continuous-time cases. With p equal to one in the discrete-time case and the number of plant outputs in the continuous-time case, we first show that for every stabilizable and detectable plant, there exists a p-dimensional linear time-varying (LTV) compensator which provides exponential stabilization; we then construct a (p+1)-dimensional NLTV controller which asymptotically stabilizes every admissible plant by switching between a countable number of such LTV compensators |
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