Node:sysprop, Next:systime, Previous:numerical, Up:Control Theory
analdemo () | Function File |
Octave Controls toolbox demo: State Space analysis demo |
[n, m, p] = abcddim (a, b, c, d) | Function File |
Check for compatibility of the dimensions of the matrices defining
the linear system
[A, B, C, D] corresponding to
dx/dt = a x + b u y = c x + d u or a similar discrete-time system. If the matrices are compatibly dimensioned, then
Otherwise Note: n = 0 (pure gain block) is returned without warning. |
ctrb (sys, b) | Function File |
ctrb (a, b) | Function File |
Build controllability matrix:
2 n-1 Qs = [ B AB A B ... A B ] of a system data structure or the pair (a, b).
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h2norm (sys) | Function File |
Computes the
H-2
norm of a system data structure (continuous time only).
Reference: Doyle, Glover, Khargonekar, Francis, State-Space Solutions to Standard H-2 and H-infinity Control Problems, IEEE TAC August 1989. |
[g, gmin, gmax] = hinfnorm (sys, tol, gmin, gmax, ptol) | Function File |
Computes the
H-infinity
norm of a system data structure.
Inputs
Outputs
References: Doyle, Glover, Khargonekar, Francis, State-space solutions to standard H-2 and H-infinity control problems, IEEE TAC August 1989; Iglesias and Glover, State-Space approach to discrete-time H-infinity control, Int. J. Control, vol 54, no. 5, 1991; Zhou, Doyle, Glover, Robust and Optimal Control, Prentice-Hall, 1996. |
obsv (sys, c) | Function File |
obsv (a, c) | Function File |
Build observability matrix:
| C | | CA | Qb = | CA^2 | | ... | | CA^(n-1) |of a system data structure or the pair (a, c). The numerical properties of |
[zer, pol] = pzmap (sys) | Function File |
Plots the zeros and poles of a system in the complex plane.
Input
Outputs
|
retval = is_abcd (a, b, c, d) | Function File |
Returns retval = 1 if the dimensions of a, b, c, d are compatible, otherwise retval = 0 with an appropriate diagnostic message printed to the screen. The matrices b, c, or d may be omitted. |
[retval, u] = is_controllable (sys, tol) | Function File |
[retval, u] = is_controllable (a, b, tol) | Function File |
Logical check for system controllability.
Inputs
Outputs
Method
Controllability is determined by applying Arnoldi iteration with
complete re-orthogonalization to obtain an orthogonal basis of the
Krylov subspace
span ([b,a*b,...,a^{n-1}*b]).The Arnoldi iteration is executed with krylov if the system
has a single input; otherwise a block Arnoldi iteration is performed
with krylovb .
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retval = is_detectable (a, c, tol, dflg) | Function File |
retval = is_detectable (sys, tol) | Function File |
Test for detactability (observability of unstable modes) of (a, c).
Returns 1 if the system a or the pair (a, c) is detectable, 0 if not, and -1 if the system has unobservable modes at the imaginary axis (unit circle for discrete-time systems). See |
[retval, dgkf_struct ] = is_dgkf (asys, nu, ny, tol ) | Function File |
Determine whether a continuous time state space system meets
assumptions of DGKF algorithm.
Partitions system into:
[dx/dt] [A | Bw Bu ][w] [ z ] = [Cz | Dzw Dzu ][u] [ y ] [Cy | Dyw Dyu ]or similar discrete-time system. If necessary, orthogonal transformations qw, qz and nonsingular transformations ru, ry are applied to respective vectors w, z, u, y in order to satisfy DGKF assumptions. Loop shifting is used if dyu block is nonzero. Inputs
is_dgkf exits with an error if the system is mixed
discrete/continuous.
References
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digital = is_digital (sys, eflg) | Function File |
Return nonzero if system is digital.
Inputs
Output
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[retval, u] = is_observable (a, c, tol) | Function File |
[retval, u] = is_observable (sys, tol) | Function File |
Logical check for system observability.
Default: tol = Returns 1 if the system sys or the pair (a, c) is observable, 0 if not. See |
is_sample (ts) | Function File |
Return true if ts is a valid sampling time (real, scalar, > 0). |
is_siso (sys) | Function File |
Returns nonzero if the system data structure sys is single-input, single-output. |
retval = is_stabilizable (sys, tol) | Function File |
retval = is_stabilizable (a, b, tol, dflg) | Function File |
Logical check for system stabilizability (i.e., all unstable modes are controllable).
Returns 1 if the system is stabilizable, 0 if the the system is not stabilizable, -1
if the system has non stabilizable modes at the imaginary axis (unit circle for
discrete-time systems.
Test for stabilizability is performed via Hautus Lemma. If dflg!=0 assume that discrete-time matrices (a,b) are supplied. |
is_signal_list (mylist) | Function File |
Return true if mylist is a list of individual strings. |
is_stable (a, tol, dflg) | Function File |
is_stable (sys, tol) | Function File |
Returns 1 if the matrix a or the system sys
is stable, or 0 if not.
Inputs
|