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dishin.m
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% DISHIN.F - Gateway function for H_infinity or H_2 design of
% discrete-time systems based on SLICOT routines
%
% [AK,BK,CK,DK,(RCOND)] = dishin(task,A,B,C,D,ncon,nmeas,(gamma))
%
% task = 1 : [AK,BK,CK,DK,(RCOND)] = dishin(1,A,B,C,D,ncon,nmeas,
% gamma)
%
% To compute the matrices of an H-infinity (sub)optimal n-state
% controller
%
% | AK | BK |
% K = |----|----|,
% | CK | DK |
%
% for the discrete-time system
%
% | A | B1 B2 | | A | B |
% P = |----|---------| = |---|---|,
% | C1 | D11 D12 | | C | D |
% | C2 | D21 D22 |
%
% and for a given value of gamma, where B2 has column size of the
% number of control inputs (ncon) and C2 has row size of the number
% of measurements (nmeas) being provided to the controller.
%
% task = 2 : [AK,BK,CK,DK,(RCOND)] = dishin(2,A,B,C,D,ncon,nmeas)
%
% To compute the matrices of the H2 optimal n-state controller
%
% | AK | BK |
% K = |----|----|,
% | CK | DK |
%
% for the discrete-time system
%
% | A | B1 B2 | | A | B |
% P = |----|---------| = |---|---|,
% | C1 | 0 D12 | | C | D |
% | C2 | D21 D22 |
%
% where B2 has column size of the number of control inputs (ncon)
% and C2 has row size of the number of measurements (nmeas) being
% provided to the controller.
%
% Input parameters:
% task - integer option to determine the type of the design:
% = 1 : H_infinity design;
% = 2 : H_2 design.
% A - the n-by-n system state matrix A.
% B - the n-by-m system input matrix B.
% C - the p-by-n system output matrix C.
% D - the p-by-m system matrix D.
% ncon - the number of control inputs. m >= ncon >= 0,
% p-nmeas >= ncon.
% nmeas - the number of measurements. p >= nmeas >= 0,
% m-ncon >= nmeas.
% gamma - (task 1 only) the parameter gamma used in H_infinity design.
% It is assumed that gamma is sufficiently large so that the
% controller is admissible. gamma >= 0.
%
% Output parameters:
% AK - the n-by-n controller state matrix AK.
% BK - the n-by-nmeas controller input matrix BK.
% CK - the ncon-by-n controller output matrix CK.
% DK - the ncon-by-nmeas controller matrix DK.
% RCOND - (optional) a vector containing estimates of the reciprocal
% condition numbers of the matrices which are to be inverted
% and estimates of the reciprocal condition numbers of the
% Riccati equations which have to be solved during the
% computation of the controller. (See the description of
% the algorithm in [1].)
%
% If task = 1 then
% RCOND(1) contains the reciprocal condition number of the
% matrix R3,
% RCOND(2) contains the reciprocal condition number of the
% matrix R1 - R2'*inv(R3)*R2,
% RCOND(3) contains the reciprocal condition number of the
% matrix V21,
% RCOND(4) contains the reciprocal condition number of the
% matrix St3,
% RCOND(5) contains the reciprocal condition number of the
% matrix V12,
% RCOND(6) contains the reciprocal condition number of the
% matrix Im2 + DKHAT*D22,
% RCOND(7) contains the reciprocal condition number of the
% X-Riccati equation,
% RCOND(8) contains the reciprocal condition number of the
% Z-Riccati equation.
%
% If task = 2 then
% RCOND(1) contains the reciprocal condition number of the
% control transformation matrix TU,
% RCOND(2) contains the reciprocal condition number of the
% measurement transformation matrix TY,
% RCOND(3) contains the reciprocal condition number of the
% matrix Im2 + B2'*X2*B2,
% RCOND(4) contains the reciprocal condition number of the
% matrix Ip2 + C2*Y2*C2',
% RCOND(5) contains the reciprocal condition number of the
% X-Riccati equation,
% RCOND(6) contains the reciprocal condition number of the
% Y-Riccati equation,
% RCOND(7) contains the reciprocal condition number of the
% matrix Im2 + DKHAT*D22 .
%
% References
% [1] P.Hr. Petkov, D.W. Gu and M.M. Konstantinov. Fortran 77 routines
% for Hinf and H2 design of linear discrete-time control systems.
% Report99-8, Department of Engineering, Leicester University,
% April 1999.
% RELEASE 2.0 of SLICOT Robust Control Toolbox.
% Based on SLICOT RELEASE 5.7, Copyright (c) 2002-2020 NICONET e.V.
%