## Abstract

A representation formula for all controllen that satisfy an P-type constraint is derived for time&varying systems. It is now known that a Cormnla based on two indefinite algebraic Rimti equations

may be found for time-invariant systems over an infinite time support (see [J. C. Doyle el al., IEEE Tmns. Automat. Confro< AC-34 (19891, pp. 831-8471; [K. Glover and 1. C. Doyle, Systems Control Len, 11 (1988), pp. 167-1721; [K. Glover et al., SIAM I. Control Optim, 29 (1991), pp.283-3241; [M. Green et al., SIAM J. Contror Optim, 28 (1990), pp. 1350-13711; [D. J. N. Limebeer et al., in Roc IEEE wnf on Decision and : , Control, Austin, TX, 19881; [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-3241). <, In the time-va~na .- case. . two indefinitk Riccati diSerential eauations are remired. A solution to the design. problem exists if these equations have a solution on the optimization interval. The derivation of the representation formula illustrated in this paper makes explicit use of Linear quadratic differential game theory and extendsthe work in [I. C. ~o~lekh.. IEEE ~rak Automat. ControcAG34(1989),pp. 831:8471 and [G. Tadmor, Malh. Control Systems Signal Rmepsing, 3 (1990). pp.301-3241. The game theoretic approach is particularly simple, in that the background mathematics required for the sufficient conditions is little more than nandard arguments based on "completing the square."

may be found for time-invariant systems over an infinite time support (see [J. C. Doyle el al., IEEE Tmns. Automat. Confro< AC-34 (19891, pp. 831-8471; [K. Glover and 1. C. Doyle, Systems Control Len, 11 (1988), pp. 167-1721; [K. Glover et al., SIAM I. Control Optim, 29 (1991), pp.283-3241; [M. Green et al., SIAM J. Contror Optim, 28 (1990), pp. 1350-13711; [D. J. N. Limebeer et al., in Roc IEEE wnf on Decision and : , Control, Austin, TX, 19881; [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-3241). <, In the time-va~na .- case. . two indefinitk Riccati diSerential eauations are remired. A solution to the design. problem exists if these equations have a solution on the optimization interval. The derivation of the representation formula illustrated in this paper makes explicit use of Linear quadratic differential game theory and extendsthe work in [I. C. ~o~lekh.. IEEE ~rak Automat. ControcAG34(1989),pp. 831:8471 and [G. Tadmor, Malh. Control Systems Signal Rmepsing, 3 (1990). pp.301-3241. The game theoretic approach is particularly simple, in that the background mathematics required for the sufficient conditions is little more than nandard arguments based on "completing the square."

Original language | English |
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Pages (from-to) | 262–283 |

Journal | SIAM Journal on Control and Optimization |

Volume | 30 |

Issue number | 2 |

Publication status | Published - 1992 |