Linear Matrix Inequalities in Optimal and Robust Control. Linear Matrix Inequalities: Discrete-time systems - HARISHANKAR PRABHAKARAN. One can find these LMIs in this book: https://arxiv.org/pdf/1903.08599.pdf . This is a set of codes as sample programs for discrete time systems in the wikibook (pages I created are listed below and the respective MATLAB codes are available): https://en.wikibooks.org/wiki/LMIs_in_Control. To run these MATLAB codes, YALMIP TOOLBOX and solvers such as SeDuMi or IBM CPLEX is Required.
A1.m - Discrete-Time Lyapunov Stability (Caverly 3.1.3) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_Lyapunov_Stability
A2.m - Discrete-Time Bounded Real Lemma (H∞ norm) (Caverly 3.2.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_Bounded_Real_Lemma
A3.m - Discrete-Time H2 Norm (Caverly 3.3.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete-Time_H2_Norm
A4.m - Discrete-Time Stabilizability (Caverly 3.11.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_Stabilizability
A5.m - Discrete-Time Detectability (Caverly 3.12.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_Detectability
A6.m - Discrete-TimeH2-Optimal Full-State Feedback Control (Caverly 4.2.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_H2_Optimal_Full_State_Feedback_Control
A7.m - Discrete-TimeH2-Optimal Dynamic Output Feedback Control (Caverly 4.2.4) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_H2_Optimal_Dynamic_Output_Feedback_Control
A8.m - Discrete-TimeH∞-Optimal Full-State Feedback Control (Caverly 4.3.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_H%E2%88%9E_Optimal_Full_State_Feedback_Control
A9.m - Discrete-TimeH∞-Optimal Dynamic Output Feedback Control (Caverly 4.3.4) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_H%E2%88%9E_Optimal_Dynamic_Output_Feedback_Control
A10.m - Discrete-Time MixedH2-H∞-Optimal Full-State Feedback Control (Caverly 4.4.2) https://en.wikibooks.org/wiki/LMIs_in_Control/pages/Discrete_Time_Mixed_H2-H%E2%88%9E_Optimal_Full_State_Feedback_Control