Delay-dependent D-stabilization conditions for linear uncertain discrete-time systems with time-delay in the states
Luís F. P. Silva1; Valter J. S. Leite1
1 CEFET-MG/Unidade Divinópolis
Resumo
We propose conditions of $\D$-stability analysis and $\D$-stabilization of linear discrete-time systems with time-delay in the states and polytopic uncertainties. The $\D$-stabilization problem consists to guarantee the regional allocation of the eigenvalues of the closed-loop systems in a $\D(\alpha,r)$ region, a circle with $\alpha$ being the center and $r$ its the radius. The conditions are based on a Lyapunov-Krasovskii candidate function and they are formulated in terms of LMIs. To achieve our contribution, we obtain an equivalent system where the eigenvalues of the original systems located in $\D(\alpha,r)$ region are mapped in the unitary circle. Therefore, if the equivalent system is Schur stable, then the original system will be $\D(\alpha,r)$-stability. We show a numerical example to illustrate the efficiency of the proposed conditions and to compare them with similar results found in the literature.
Palavras-chave: Linear discrete-time systems with time-delay in the states and polytopic uncertainties; $\D$-stability; Lyapunov-Krasovskii candidate function; LMIs