Linear Matrix Inequalities (LMIs) and LMI techniques have emerged as powerful design tools in areas ranging from control engineering to system identification and structural design. Three factors make LMI techniques appealing:
A variety of design specifications and constraints can be expressed as LMIs.
Once formulated in terms of LMIs, a problem can be solved exactly by efficient convex optimization algorithms (see LMI Solvers).
While most problems with multiple constraints or objectives lack analytical solutions in terms of matrix equations, they often remain tractable in the LMI framework. This makes LMI-based design a valuable alternative to classical “analytical” methods.