In this paper, a class of linear infinite-dimensional systems with discrete and distributed time-varying delays is studied. New sufficient conditions for the robust H ∞ control of linear time-varying control systems with mixed time-varying delays in Hilbert spaces have been established. The conditions are given in terms of the solution of a Riccati differential equation. Furthermore, it is proved for the first time that the solution to the robust H ∞ control problem can be solved by the global controllability of an appropriate linear control delay-like system.ROBUST H ∞ CONTROL OF LINEAR TIME-VARYING SYSTEMS 547 E(t), D(t), t 0, are given linear operator-valued functions; the delay functions h(t), k(t) satisfy the following condition:
Proposition 2.3 (Phat [16]) If linear control system [A(t), B(t)]is globally null-controllable in some finite time, then for any Q ∈ BC([0, ∞), X + ) ROE (4), where R(t) = B(t)B * (t), has a solution P ∈ BC([0, ∞), X + ).We conclude this section with the following technical proposition for later use.
We present some conditions for the asymptotic equilibrium of nonlinear differential equations and, in particular, a linear inhomogeneous equation in Banach spaces. We also discuss analogous problems for a linear equation with unbounded operator. Some obtained results are applied to problems of asymptotic equivalence.Hanoi, Vietnam.
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