Ph.D. received on: 16/4/1998

E-mail: carpanev@dei.unipd.it

Tutor: Prof. M. Bisiacco, Università di Padova
 
 

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Models for 1D and 2D periodic systems   ___________________________________________________________________________________________________________

Advisor:

Prof. M. Bisiacco, Università di Padova
 

Summary:

Periodic systems theory is a well-established field of investigation, the reason being the aim of applications in modeling and control of plants. However this theory substantially lacks in the 2D framework which is basically developed with the same aim. Also the appealing J.C.Willems’ model theory, namely the behavioral approach, seems to be promising of fruitful applications in the periodic context even in the 1D case. Recent papers pursued this goal by extending 1D lifting and twisting techniques of periodic setting in the behavioral framework.
In this work both these points are developed. For 2D periodic systems the 2D lifting isomorphism is introduced: to any 2D periodic system having state dimension equal to n an appropriate 2D invariant system corresponds (having state dimension equal to nT if T is the period of the original system). Within this framework the study of state space issues (stability, asymptotic and/or non-asymptotic controllability and/or reconstructability) is carried out.
For 1D systems the contribution of the thesis can be outlined with reference to the well-known Floquet-Lyapunov theory in which special type of transformations convert a time varying continuos system into an invariant one. The discrete time counterpart is explored: from a periodic behavior an invariant behavior is simply obtained by sampling its trajectories with a time step equal to its period. This tool may prove to be useful. In fact in this thesis the periodic Riccati difference equation (PRDE) is considered as a case study since the geometric characterization in terms of generalized invariant subspaces of its periodic solutions can be embedded in the behavioral approach. In this work it is showed how the parameterization of  the solutions of PRDE can be obtained by resorting to this tool extending the well-known Willems-Coppel-Shayman characterization.

 

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