Convex optimization for linear matrix inequalities

  • Is linear matrix inequality convex?

    This linear matrix inequality specifies a convex constraint on y.Sep 21, 2016.

  • What is the feasibility of linear matrix inequality?

    There are three generic problems related to the study of linear matrix inequalities: Feasibility: The test whether or not there exist solutions x of F(x) \x26gt; 0 is called a feasibility problem.
    The LMI is called non-feasible if no solutions exist..

  • What is the LMI approach?

    There is actually another way to consider the robust design problem, and control system design in general, as an optimization problem, solutions to which can be directly computed by convex computational procedures.
    That is the so called Linear Matrix Inequality (LMI) approach..

  • There are three generic problems related to the study of linear matrix inequalities: Feasibility: The test whether or not there exist solutions x of F(x) \x26gt; 0 is called a feasibility problem.
    The LMI is called non-feasible if no solutions exist.
  • There is actually another way to consider the robust design problem, and control system design in general, as an optimization problem, solutions to which can be directly computed by convex computational procedures.
    That is the so called Linear Matrix Inequality (LMI) approach.
The cost is linear and the set of feasible decisions is defined by finitely many affine inequality constraints.

Is a linear matrix inequality a convex constraint?

1

Introduction A linear matrix inequality (LMI) is a convex constraint

Consequently, optimization problems with convex objective functions and LMI constraints are solvable relatively efficiently with off-the-shelf software

The form of an LMI is very general

What are convex nonlinear inequalities?

The convex nonlinear inequalities are (27) R x >0, Q x −S x R x −1 S x T >0, where Q x =Q x T ,R x =R x T, and S x depend affinely on x

The Schur complement lemma converts this set of convex nonlinear inequalities into the equivalent LMI (28) Q x S x S x T R x >0

What is a linear matrix inequality technique?

LMI (linear matrix inequality) techniques offer more flexibility in the design of dynamic linear systems than techniques that minimize a scalar functional for optimization

For linear state space models, multiple goals (performance bounds) can be characterized in

Linear Matrix Inequality Techniques in Optimal Control | SpringerLink


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