Iterative Dual Rational Krylov and Iterative SVD-Dual Rational Krylov Model Reduction for Switched Linear Systems - Complex System Modelling and Control Through Intelligent Soft Computations - page 428

and the Tolerance(Tol) for both models. Seeing the values of H 1 error for two
models obtained by the iterative SVDDRK-SLS method are better then obtained by
the iterative DRK-SLS method, also be seen that the CPU-time and the tolerance
differs from one method to another, they are mainly dependent on the order model.

7 Conclusion

In this chapter, two methods for reduction of linear switched systems have been
proposed. At first the iterative dual rational Krylov method based on generation of

Krylov subspaces is presented. This method have low cost, but the stability of
reduced system not always guaranteed.
In the second part, the iterative SVD-Dual rational Krylov based on the SVD and
Krylov subspace techniques in generating of the projection matrices V r q and Z r q for
each subsystem is presented. This method is numerically ef

cient using the Krylov
technique and guaranteed the stability of each reduced subsystems using the
observability matrix obtained from the Lyaponuv equation.
To evaluate the accuracy and ef

cient of these methods, a numerical examples is

presented.
As a future works the development and validation of control algorithms for
switched linear system based on reduces models obtained by Iterative DRK-SLS
and Iterative SVDDRK-SLS methods is recommended. The implementation of the
control algorithm determined from the reduced systems obtained by the dual
rational Krylov methods on a microcontroller to control the original switched
system is proposed. Addaptation of the previous methods to be applied on non-
linear systems and on the other hybrid systems is also proposed.

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