LPVSYN - Parameter-dependent controller synthesis for LPV systems

Contents

Syntax

  [K,GAM,INFO] = lpvsyn(P,NMEAS,NCON)
  [K,GAM,INFO] = lpvsyn(P,NMEAS,NCON,Xb,Yb)
  [K,GAM,INFO] = lpvsyn(P,NMEAS,NCON,...,OPT)

Description

[K,GAM,INFO] = lpvsyn(P,NMEAS,NCON) computes a parameter-varying controller K which minimizes the induced $L_2$ norm of the interconnection defined by lft(P,K). K is a pss or plftss with NMEAS inputs and NCON outputs, defined on same domain as P. GAM is the induced $L_2$ norm of lft(P,K). This three argument call assumes that the rate-bounds of the independent variables in P are [-inf,inf]. INFO is a structure containing data from the Linear Matrix Inequalities that are solved to obtain K.

[K,GAM,INFO] = lpvsyn(P,NMEAS,NCON,Xb,Yb) computes the rate-bounded parameter-varying controller K for a system P. K is the controller which minimizes the induced $L_2$ norm of lft(P,K) when the rate-bounds of the independent variables of P are incorporated into the synthesis. Xb and Yb are basis objects, which describe the assumed parameter dependence of the lyapunov matrices used in solving for K.

[K,GAM,INFO] = lpvsyn(P,NMEAS,NCON,...,OPT) allows the user to pass in a lpvsynoptions object.

The default algorithm for lpvsyn will solve the given synthesis problem twice. The first iteration attempts to find a solution that minimizes the induced $L_2$ norm of lft(P,K). The second iteration will solve the optimization problem again, with the caveat that any solution that is % found to lie within 15% of the optimal induced $L_2$ norm of lft(P,K) from the first iteration, is satisfactory. This formulation has been found to yield controllers that are better numerically conditioned. The back-off factor of 15% can be reset to a different value in lpvsynoptions.