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LMI characterization of structural and robust stability: The discrete-time case. (English) Zbl 0949.93063

Authors’ abstract: This paper extends to the discrete-time case some robust stability conditions, recently obtained for continuous-time systems. Those conditions are expressed in terms of Linear Matrix Inequalities (LMI), being thus simply and efficiently computable. As in the continuous-time case, parameter-dependent Lyapunov functions can be constructed and, consequently, the new approach can yield much sharper and less conservative results than the simultaneous stability approach. In particular, well-known stability problems, namely, D-stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed. Numerical examples are included to illustrate the advantages of the new stability conditions.

MSC:

93D09 Robust stability
93C55 Discrete-time control/observation systems
15A39 Linear inequalities of matrices
15A42 Inequalities involving eigenvalues and eigenvectors
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