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Abstract: Joint estimation of states and events in linear regime-switching systems is studied under irregular sampling schemes which stem from improved sampling and quantization methods for efficient utility of communication resources. Joint observability and sampling complexity are established, extending Shannon’s sampling theorem and our recent results on sampling complexity to joint estimation problems. Observer design and convergence analysis are conducted for systems under noisy observations. It is shown that our algorithms converge strongly with an error bound of the order . Simulation examples are included to illustrate potential usages of the algorithms. [Copyright &y& Elsevier]

Abstract: System identification of plants with binary-valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information, establishing relationships between communication resource limitations and identification complexity, and studying sensor networks. This paper resolves two issues arising in such system identification problems. First, regression structures for identifying a rational model contain non-smooth nonlinearities, leading to a difficult nonlinear filtering problem. By introducing a two-step identification procedure that employs periodic signals, empirical measures, and identifiability features, rational models can be identified without resorting to complicated nonlinear searching algorithms. Second, by formulating a joint identification problem, we are able to accommodate scenarios in which noise distribution functions are unknown. Convergence of parameter estimates is established. Recursive algorithms for joint identification and their key properties are further developed. [Copyright &y& Elsevier]