Fonctionnelles causales non linéaires et indéterminées non commutatives
Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems [Book]
Generalized Bezoutian for a periodic collection of rational matrices
Generating series and nonlinear systems: Analytic aspects, local realizability, and i/o representations.
control design for an adaptive optics system
In this paper we first present a full order controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order controller and demonstrate that the closed-loop (CL) system with the reduced order controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order controller it is found that the dynamical behavior of the reduced order controller can be accurately approximated by...
Hankel-matrix approach to invertibility of linear multivariable systems
Input-output decoupling of nonlinear recursive systems
The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i. e. for systems, modelled by higher order nonlinear difference equations, relating the input, the output and a finite number of their time shifts. The solution of the problem via regular static feedback known for discrete-time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed. This is the alternative to...
Input-output systems, their types and applications for the automata theory
J-energy preserving well-posed linear systems
The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems:...
Linear dynamical systems of higher genus.
Linearization by completely generalized input-output injection
The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed...
Minimal positive realizations: a survey of recent results and open problems
In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions...
Minimal realization for positive multivariable linear systems with delay
The realization problem for positive multivariable discrete-time systems with one time delay is formulated and solved. Conditions for the solvability of the realization problem are established. A procedure for the computation of a minimal positive realization of a proper rational matrix is presented and illustrated by an example.
Minimal realizations of the inverse of a polynomial matrix using finite and infinite Jordan pairs
Nonlinear approximation in control problems
Nonregular decoupling with stability of two-output systems
In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list is greater than or equal to the infinite and unstable structure of the proper and stable...
On minimal realizations and minimal partial realizations of linear time-invariant systems subject to point incommensurate delays.
On state space representations of AR-models.
On the nature of descriptor systems
On the realization theory of polynomial matrices and the algebraic structure of pure generalized state space systems
We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out...