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Estimation of states and events in randomly switching systems is studied under irregular and random sampling schemes. Probabilistic characterization of observability is presented under various sampling schemes and regime-switching processes. The characterization is derived on the basis of our recent results on sampling complexity for system observability. Observer design and algorithms are developed. 1. Introduction. This paper investigates estimation of states and events in ran- domly switching systems under various sampling schemes. The problems are typically studied under the names of regime-switching systems, hybrid systems, discrete-event systems, etc. Typically, such systems involve communication channels whose power and bandwidth limitations make it desirable to reduce resource consumption in sam- pling and quantization. It was shown in (29, 30) that traditional periodic sampling is inefficient in utility of such resources. More efficient sampling/quantiz ation schemes introduced in (29, 30) lead naturally to irregular sampling (also known as non-uniform or non-periodic sampling). Irregular and random sampling may occur also due to event triggered sampling (3, 22) or communication uncertainty and interruptions (9). When a system switches its dynamics, it introduces an event which is itself a dy- namic process whose state space is a finite set and its state also needs to be estimated. State estimation of linear dynamic systems is a traditional topic that has been well studied (14). Independently, observability of events has been studied extensively in discrete event systems (15, 18). References (25, 26) contain more recent studies on observability of sampled systems. Joint identification of states and events has been studied in hybrid systems (20, 25). Studies on fundamental properties of non-uniform sampling remain an active area of research, see (6) and the references therein for some recent work in this area. Some related results on identification, state estimation, and fault detection using binary or quantized outputs can be found in (13, 26, 31, 32, 35). This paper studies some fundamental issues in joint estimation of states and events when the events are stochastic processes. The main issues are: What are the conditions for observability? How many sampling points are needed to ensure

State and event estimation for regime-switching systems under irregular and random sampling schemes