Abstract

. This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well. 1 Introduction - The Need for Hybrid Systems Linear control theory is well-developed and highly sophisticated, and is widely applied in areas ranging from aerospace to automotive control. Linear systems provide highly accurate models of many physical systems; furthermore, the use of linear systems as "robust" controllers often allows the tolerance of even severe model nonlinearities and uncertainties. However, it remains a fact that many continuous physical processes cannot be satisfactorily modeled linearly, nor can be adequately regulated by means of linear controllers alone. It has long been recognized that the control of more complex systems than those handled by the linear theory will require switching mechanisms (disco...

Citations

286	Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition - Sontag - 1998
139	On the computational power of neural nets - Siegelmann, ED - 1995
112	Nonlinear regulation: the piecewise linear approach - Sontag - 1981
56	A general result on the stabilization of linear systems using bounded controls - Sussmann, Sontag, et al. - 1994
26	Remarks on continuous feedback, in - Sontag, Sussmann - 1980
25	Analog computation, neural networks, and circuits - Siegelmann, Sontag - 1994
21	Remarks on piecewise-linear algebra - Sontag - 1982
15	Real addition and the polynomial hierarchy - Sontag - 1985
13	State observability in recurrent neural networks - Albertini, Sontag - 1994
6	Identifiability of discrete-time neural networks - Albertini, Sontag - 1993
6	Systems combining linearity and saturations and relations to neural networks - Sontag - 1992
5	Observability of linear systems with saturated outputs - Koplon, Hautus, et al. - 1994
2	Sign-linear systems as cascades of automata and continuous variable systems - Koplon, Sontag - 1993
2	Systems combining linearity and saturations, and relations to "neural nets - Sontag - 1992