Coalgebraic Foundations of Linear Systems

Viewing discrete-time causal linear systems as (Mealy) coalgebras, we describe their semantics, minimization and realisation as universal constructions, based on the final coalgebras of streams and causal stream functions.

[1]  Michael A. Arbib,et al.  Foundations of system theory: Decomposable systems , 1974, Autom..

[2]  Jan J. M. M. Rutten,et al.  Algebraic Specification and Coalgebraic Synthesis of Mealy Automata , 2006, FACS.

[3]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[4]  Edward A. Feigenbaum,et al.  Switching and Finite Automata Theory: Computer Science Series , 1990 .

[5]  Eduardo Sontag Polynomial Response Maps , 1979 .

[6]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[7]  M. Arbib,et al.  Adjoint machines, state-behavior machines, and duality☆ , 1975 .

[8]  Jan J. M. M. Rutten,et al.  Behavioural differential equations: a coinductive calculus of streams, automata, and power series , 2003, Theor. Comput. Sci..

[9]  George J. Pappas Bisimilar linear systems , 2003, Autom..

[10]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .

[11]  Jan J. M. M. Rutten,et al.  A tutorial on coinductive stream calculus and signal flow graphs , 2005, Theor. Comput. Sci..

[12]  Jan J. M. M. Rutten,et al.  Synthesis of Mealy Machines Using Derivatives , 2006, CMCS.

[13]  Michael A. Arbib Fondations de la théorie de systèmes: Systèmes décomposablesGrundlagen der systemtheorie: Dekomponierbare systemeФopмиpoвaниe тeopии cиcтeм: дeкoмпoзaбeльнe cиcтeмы , 1974 .

[14]  Arjan van der Schaft,et al.  Equivalence of dynamical systems by bisimulation , 2004, IEEE Trans. Autom. Control..

[15]  P. Fuhrmann A Polynomial Approach to Linear Algebra , 1996 .

[16]  G. Birkhoff,et al.  A survey of modern algebra , 1942 .

[17]  R. Kálmán Mathematical description of linear dynamical systems , 1963 .

[18]  Thomas Kailath,et al.  Linear Systems , 1980 .