Robust Control Toolbox™

Multi-model/multi-objective state-feedback synthesis

Syntax

• [gopt,h2opt,K,Pcl,X] = msfsyn(P,r,obj,region,tol) 
  

Description

Given an LTI plant P with state-space equations

msfsyn computes a state-feedback control u = Kx that

• Maintains the RMS gain (H norm) of the closed-loop transfer function T from w to z below some prescribed value
• Maintains the H2 norm of the closed-loop transfer function T2 from w to z2 below some prescribed value
• Minimizes an H2/H trade-off criterion of the form

• Places the closed-loop poles inside the LMI region specified by region (see lmireg for the specification of such regions). The default is the open left-half plane.

Set r = size(d22) and obj = [0, 0, , ] to specify the problem dimensions and the design parameters 0, 0, , and . You can perform pure pole placement by setting obj = [0 0 0 0]. Note also that z or z2 can be empty.

On output, gopt and h2opt are the guaranteed H and H2 performances, K is the optimal state-feedback gain, Pcl the closed-loop transfer function from w to , and X the corresponding Lyapunov matrix.

The function msfsyn is also applicable to multi-model problems where P is a polytopic model of the plant:

with time-varying state-space matrices ranging in the polytope

In this context, msfsyn seeks a state-feedback gain that robustly enforces the specifications over the entire polytope of plants. Note that polytopic plants should be defined with psys and that the closed-loop system Pcl is itself polytopic in such problems. Affine parameter-dependent plants are also accepted and automatically converted to polytopic models.

See Also
lmireg      Specify LMI regions for pole placement purposes

psys        Specification of uncertain state-space models

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