Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et séries génératrices non commutatives.
In this paper differential forms and differential algebra are applied to give a new definition of realization for multivariable nonlinear systems consistent with the linear realization theory. Criteria for the existence of realization and the definition of minimal realization are presented. The relations of minimal realization and accessibility and finally the computation of realizations are also discussed in this paper.
The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.
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 characterization of minimal realizations is presented. The paper treats two types of switched systems. The...
This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...
This paper is the second part of a series of papers dealing with realization theory of switched systems. The current Part II addresses realization theory of bilinear switched systems. In Part I [Petreczky, ESAIM: COCV, DOI: 10.1051/cocv/2010014] we presented realization theory of linear switched systems. More precisely, in Part II we present necessary and sufficient conditions for a family of input-output maps to be realizable by a bilinear switched system, together with a characterization of minimal...
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 characterization of minimal realizations is presented. The paper treats two types of switched systems. The...
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.