There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

http://ieeexplore.ieee.org/iel5/5610941/5624686/05624745.pdf

Power electronics

Feedback systems: Input-output properties

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Stochastic Processes And Filtering Theory

Robust stabilization of uncertain descriptor fractional-order systems

https://hal.archives-ouvertes.fr/hal-00751553/document

Observer design for one-sided Lipschitz discrete-time systems

This simple algorithm for the state estimation of stochastic singular linear systems is based on the least squares method.

/pdf/state-estimation-of-stochastic-singular-linear-systems-3xz7rz5rfa.pdf

State estimation of stochastic singular linear systems

A generalized linear dynamic model or singular model, for which the standard state space representation and the Kalman filtering cannot be applied, is used to develop a new algorithm to solve the linear dynamic material balance problem. This algorithm is based on the method developed in the steady-state case and leads to a recursive scheme, which is very useful in real-time processing. It reduces the computational problem such as singularities and round-off errors that may occur in complex systems. Convergence conditions are given and verified for the dynamic material balance case.

https://hal.archives-ouvertes.fr/hal-00143553/document

Data reconciliation in generalized linear dynamic systems

This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1źα<2 and 0<αź1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.

/pdf/design-of-unknown-input-fractional-order-observers-for-3bpvf6sxfi.pdf

Michel Zasadzinski

Papers

Robust stabilization of uncertain descriptor fractional-order systems

Observer design for one-sided Lipschitz discrete-time systems

State estimation of stochastic singular linear systems

Data reconciliation in generalized linear dynamic systems

Design of unknown input fractional-order observers for fractional-order systems