Realization Theory For Linear and Bilinear Hybrid Systems
نویسنده
چکیده
The paper deals with the realization theory of linear and bilinear hybrid systems, i.e. hybrid systems with continuous dynamics determined by linear ( respectively bilinear ) control systems. We will formulate necessary and sufficient conditions for the existence of a linear (bilinear ) hybrid system realizing the specified input/output maps. We will also present a characterization of a minimal linear (bilinear) hybrid realization and a procedure to convert a linear (bilinear) hybrid system to a minimal one. Partial realization of linear (bilinear) hybrid systems will be discussed too. 2000 Mathematics Subject Classification: 93B15, 93B20, 93B25, 93C99
منابع مشابه
Hybrid Formal Power Series and Their Application to Realization Theory of Hybrid Systems
The paper presents the abstract framework of hybrid formal power series. Hybrid formal power series are analogous to non-commutative formal power series. Formal power series are widely used in control systems theory. In particular, theory of formal power series is the main tool for solving the realization problem for linear and bilinear control systems. The theory of hybrid formal power series ...
متن کاملRealization Theory of Bilinear Hybrid Systems
The paper deals with the realization theory of bilinear hybrid systems, i.e. hybrid systems with continuous dynamics determined by bilinear control systems. We will formulate necessary and sufficient conditions for the existence of a bilinear hybrid system realizing a set of specified input/output maps. We will also present a characterization of a minimal bilinear hybrid realization and a proce...
متن کاملSpan-reachability and observability of bilinear hybrid systems
The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics is determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and spanreachability in ter...
متن کاملModelling, Analysis and Simulation Modelling, Analysis and Simulation Realization theory for linear and bilinear switched systems: a formal power series approach
The paper deals with the realization theory of linear and bilinear switched systems. Necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a (bi)linear switched system. Characterization of minimal realizations is presented. The paper treats two types of (bi)linear switched systems. The first one is when all switching sequences are allowed. The ...
متن کاملRealization Theory for Linear and Bilinear Switched Systems: a Formal Power Series Approach Part I: Realization Theory of Linear Switched Systems
The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a chara...
متن کامل