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For linear time-invariant systems with one or more noncommensnrate time delays, necessary and sufficient conditions are given for the existence of, a fiite-dimensional stabilizing feedback compensator. In particular, it is shown that a stabilizable time-delay system can always be stabilized using a finite-dimensional compensator. The problem of explicitly constructing finite-dimensional stabilizing compensators is also considered. I. STABILIZATION OF SYSTEMS WITH DELAYSIn this note we consider the problem of stabilizing a linear timeinvariant continuous-time system with q noncommensurate time delays h,, hZ, .-., h,. The systems we shall study are given by a state representation of the form dt y((t)=(ff(db,, dbp " ' I dh8)x)(r)+(J(dh,. dhz, dhq)U)(f) (1.1)where the m-vector u(t) is the input at time t, the n-vector x(t) is the instantaneous state at time t , the p-vector y(r) is the output at time t, and matrices whose entries are polynomials in the delay operators dh,, . . . , dhq with coefficients in the reds m. (Here (d&f)(t)= Atrhi) for any positive integer r.)

Aktruct-State feedback control of slowly-varying linear continuoustime and discrete-time systems with bounded coefficient matrices is studied in terms of the frozen-time approach. This note centers on pointwise stabilizable systems: that is, systems for which there exists a state feedback gain matrix placing the frozen-time closed-loop eigenvalues to the left of a line Res =y < 0 in the complex plane (or within a disk of radius p < 1 in the discrete-time case). It is shown that if the entries of a pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.It is also shown that for pointwise stabilizable systems with a sufficiently slow rate of time variation in the system coefficients, a stabilizing feedback gain matrix can be computed from the positive definite solution of a frozen-time algebraic Riccati equation.