Linear Matrix Inequalities

LMI solvers, control system analysis and design with LMIs

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.

Functions

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 `lmiedit` Specify or display systems of LMIs as MATLAB expressions `setlmis` Initialize description of LMI system `lmivar` Specify matrix variables in LMI problem `lmiterm` Specify term content of LMIs `newlmi` Attach identifying tag to LMIs `getlmis` Get internal description of LMI system `dellmi` Remove LMI from system of LMIs `delmvar` Remove one matrix variable from LMI problem `setmvar` Instantiate matrix variable and evaluate all LMI terms involving this matrix variable
 `lmiinfo` Information about variables and term content of LMIs `lminbr` Return number of LMIs in LMI system `matnbr` Number of matrix variables in system of LMIs `decnbr` Total number of decision variables in system of LMIs `dec2mat` Given values of decision variables, derive corresponding values of matrix variables `mat2dec` Extract vector of decision variables from matrix variable values `decinfo` Describe how entries of matrix variable X relate to decision variables
 `feasp` Compute solution to given system of LMIs `mincx` Minimize linear objective under LMI constraints `defcx` Help specify cTx objectives for `mincx` solver `gevp` Generalized eigenvalue minimization under LMI constraints
 `evallmi` Given particular instance of decision variables, evaluate all variable terms in system of LMIs `showlmi` Return left and right sides of LMI after evaluation of all variable terms
 `hinfgs` Synthesis of gain-scheduled H∞ controllers `hinfsyn` Compute H-infinity optimal controller `h2hinfsyn` Mixed H2/H∞ synthesis with regional pole placement constraints `msfsyn` Multi-model/multi-objective state-feedback synthesis