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Multi-model/multi-objective state-feedback synthesis


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


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 γ0 > 0

  • Maintains the H2 norm of the closed-loop transfer function T2 from w to z2 below some prescribed value υ0 > 0

  • 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 = [γ0, ν0, α, β] to specify the problem dimensions and the design parameters γ0, ν0, α, and β. 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 (zz2), 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

(A(t)B1(t)B2(t)C1(t)D11(t)D12(t)C2(t)0D22(t)) Co{(AkBkCkC1kD11kD12kC2k0D22k):k=1,...,K}

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.

Version History

Introduced before R2006a

See Also