Adaptive State Observers of Linear Time-Varying Descriptor Systems: A Parameter Estimation-Based Approach

In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters. We proceed from the general description of the system given by the Standard Canonical Form and try to develop a comprehensive theory for the design of adaptive observers for these systems. A consequence of our intention to keep the analysis as general as possible is that the final results are a little bit cryptic. Certainly, proceeding from this general framework, we can address particular cases and achieve some practically workable designs. We have identified several critical aspects of the problem. For instance, the highly relevant role played by the strangeness index and underscore the differences between the time-variant and the time-invariant cases, which are quite significant. We give simulation results of benchmark examples that illustrate the performance of the proposed adaptive observer.