Tan, Zhiqiang; Soh, Yeng Chai; Xie, Lihua Dissipative control for linear discrete-time systems. (English) Zbl 0949.93068 Automatica 35, No. 9, 1557-1564 (1999). The paper considers the “equation + index” system \[ x_{k+1}= Ax_k+B_1u_k \]\[ z_k=C_1x_k+ D_{11}u_k \]\[ E(u,z,N)= \sum^N_0(z^*_k Qz_k+2x_k Su_k+ u^*_kRu_k). \] A review of dissipativity theory is given for such systems. Then one considers the two-input/two-output system \[ x_{k+1}= Ax_k+B_1 \omega_k+B_2u_k \]\[ z_k=C_1x_k+ D_{11}\omega_k +D_{12}u_k \]\[ y_k=C_2 x_k+D_{21} \omega_k. \] A Linear Matrix Inequalities (LMI) approach is used to obtain the feedback control \(u_k=Kx_k\) so that the resulting system should be dissipative and exponentially stable. An example is given. Reviewer: Vladimir Răsvan (Craiova) Cited in 28 Documents MSC: 93D15 Stabilization of systems by feedback 15A39 Linear inequalities of matrices 93D10 Popov-type stability of feedback systems 93C55 Discrete-time control/observation systems Keywords:discrete-time systems; feedback stabilization; linear matrix inequalities; dissipativity; feedback control PDF BibTeX XML Cite \textit{Z. Tan} et al., Automatica 35, No. 9, 1557--1564 (1999; Zbl 0949.93068) Full Text: DOI OpenURL