Derivation of the maximum entropyH_∞-controller and a state-space formula for its entropy

Observer-based compensators for fixed-order H∞control

“…This physical meaning may be interpreted as follows. It is known that the Hz norm of the strictly proper part (without the feedback forward gain Dl,) of the closed-loop transfer function of the system (2.3) is bounded from above by the absolute value of the entropy at infinity, that is For a definition of entropy and the fact that the right-hand side of (2.9) is the negative of the entropy at infinity, see Glover and Mustafa (1989) or Mustafa and Glover (1990). An H , controller of order r is said to be ' H , / H , minimal' if there is no H , controller of order less than r satisfying the same y bound as in (2.6) and yielding the same Hz performance bound J, defined in (2.9).…”

A LQG Control Problem with Degree and Robustness Constraints

“…However, all these conditions are given in terms of coupled Riccati equations and there are no effective procedures to solve them. Mustafa has shown that the maximum entropy H ∞ control problem [10] approximates a special mixed H 2 /H ∞ control problem in which z 1 and z 2 are the same. In this case the so-called "central controller" minimizes an upper bound of the H 2 norm [11].…”

Synchronization of unified chaotic system by sliding mode/mixed H 2/H ∞ control

“…One way to solve the mixed problem is to replace the H 2 norm by a suitable upper bound. The maximum entropy method [16], the auxiliary cost method [17], and the method proposed by Doyle et al in [18] used this approach. Khargonekar and Rotea [19] gave an efficient convex optimization formulation using the auxiliary cost function of [17].…”