This linear matrix inequality specifies a convex constraint on y.

In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality.

It establishes a relation between a linear matrix inequality involving the state space constructs A, b, c and a condition in the frequency domain.

In automatic control theory, SDP's are used in the context of linear matrix inequalities.

An optimization-based reformulation of the Riccati equation uses Linear matrix inequalities and requires fewer assumptions.

This is a linear matrix inequality (LMI) feasibility test, which is a convex optimization problem.

Linear matrix inequality (LMI)

This work provided the foundation for numerous researchers in the 1990s to address advances in fixed-order control via Linear Matrix Inequalities (LMIs).

When the constraints are convex (e.g. in semidefinite problems involving LMIs, Linear Matrix Inequalities), the theoretical results are tight.

For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov functions for physical system.

It is uniquely effective in manipulating the convex hull of polytopic forms, and, hence, has revealed and proved the fact that convex hull manipulation is a necessary and crucial step in achieving optimal solutions and decreasing conservativeness in modern linear matrix inequality based control theory.