TY - GEN

T1 - Control system analysis and synthesis via linear matrix inequalities

AU - Boyd, S.

AU - Balakrishnan, V.

AU - Feron, E.

AU - ElGhaoui, L.

N1 - Generated from Scopus record by KAUST IRTS on 2021-02-18

PY - 1993/1/1

Y1 - 1993/1/1

N2 - A side variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are 'analytical solutions' to these problems, but in general they can be solved numerically very efficiently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number of Lyapunov or Algebraic Riccati equations. Therefore the computational cost of extending current control theory that is based on the solution of algebraic Riccati equations to a theory based on the solution of (multiple, simultaneous) Lyapunov or Riccati inequalities is modest. Examples include: multicriterion LQG, synthesis of linear state feedback for multiple or nonlinear plants ('multi-model control'), optimal transfer matrix realization, norm scaling, synthesis of multipliers for Popov-like analysis of systems with unknown gains, and many others. Full details can be found in the references cited.

AB - A side variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are 'analytical solutions' to these problems, but in general they can be solved numerically very efficiently. In many cases the inequalities have the form of simultaneous Lyapunov or algebraic Riccati inequalities; such problems can be solved in a time that is comparable to the time required to solve the same number of Lyapunov or Algebraic Riccati equations. Therefore the computational cost of extending current control theory that is based on the solution of algebraic Riccati equations to a theory based on the solution of (multiple, simultaneous) Lyapunov or Riccati inequalities is modest. Examples include: multicriterion LQG, synthesis of linear state feedback for multiple or nonlinear plants ('multi-model control'), optimal transfer matrix realization, norm scaling, synthesis of multipliers for Popov-like analysis of systems with unknown gains, and many others. Full details can be found in the references cited.

UR - https://ieeexplore.ieee.org/document/4793262/

UR - http://www.scopus.com/inward/record.url?scp=0027836078&partnerID=8YFLogxK

U2 - 10.23919/acc.1993.4793262

DO - 10.23919/acc.1993.4793262

M3 - Conference contribution

SN - 0780308611

SP - 2147

EP - 2154

BT - American Control Conference

PB - Publ by IEEEPiscataway

ER -