LMIs in Control/Click here to continue/LMIs in system and stability Theory/General LMI Region D-Admissibility

The System Consider . The pair (,) is D-admissible if it is regular and causal, and the eigenvalues of (,) lie within the LMI region D of the complex plane, which is defined as , where , and is the complex complex conjugate of . Conditions The pair (,) is D-admissible if and only if any of the following equivalent conditions are satisfied. There exist where rankand satisfying There exist where satisfying and There exist where rank and satisfying There exist where rank and satisfying where is the Kroenecker product and is an matrix filled with ones. There exist where satisfying and where is the Kroenecker product and is an matrix filled with ones. There exist where rank and satisfying where is the Kroenecker product and is an matrix filled with ones. Reference Caverly, Ryan; Forbes, James (2021). LMI Properties and Applications in Systems, Stability, and Control Theory.