Henri Bourlès

Periodic-polynomial interpretation for structural properties of linear periodic discrete-time systems

The structural properties of linear periodic discrete-time systems are analyzed in the periodic polynomial representation. It is shown that the classical polynomial approach for linear time-invariant systems can be extended to periodic systems. New definitions and properties are given in terms of skew polynomial rings and periodic difference algebra. Necessary and sufficient conditions for the characterization of reachability, controllability, observability and reconstructibility are given in this framework.

An intrinsic algebraic setting for poles and zeros of linear time-varying systems

In this paper, poles and zeros are defined for linear time-varying systems using suitable ground field extensions. The definitions of the system poles, transmission poles, invariant zeros, hidden modes, etc, are given in an intrinsic module-based framework and are consistent in the sense that the poles are connected to the stability of the system and the zeros to the zeroing of the output for non zero inputs. In particular, it is proved that the necessary and sufficient condition for a continuous-time system to be exponentially stable is similar to the well-known condition in the time-invariant case.

Duality for Differential-Difference Systems over Lie Groups

In modern mathematical systems theory, there exist two consistent ways of defining and describing a linear system: (i) in the behavioral approach, a linear system is the kernel

Elimination, fundamental principle and duality for analytic linear systems of partial differential-difference equations with constant coefficients

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On the existence of minimal and canonical realizations of linear periodic discrete time systems

of a matrix-valued operator

Algebraic theory of linear periodic discrete-time systems in their polynomial matrix and module descriptions

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Robust stabilization of discrete-time periodic linear systems for tracking and disturbance rejection

in a power of a signal space

Quasi-poles of linear time-varying systems in an intrinsic algebraic approach

W

Robust feedback linearization without full state information

; (ii) in the module-theoretic setting, a linear system is the cokernel

POLES OF LINEAR TIME-VARYING SYSTEMS REVISITED

M