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In this paper, we study the robust stability of uncertain time-delay systems. We consider uncertain quasi-polynomials whose coefficients may vary in a certain prescribed range. Our goal is to derive necessary and sufficient conditions for such uncertain quasi-polynomials to maintain stability independent of delay parameters. Our primary contributions are frequency-sweeping conditions for interval, diamond, and spherical quasi-polynomial families, which can be readily checked, requiring only the computation of two simple frequency-dependent functions. Additionally, we also obtain vertex- and edge-type results in the spirit of the Kharitonov approach known in robust stability analysis, showing that the stability of interval and diamond quasi-polynomials can be ascertained by checking the stability of certain special vertex and/or edge members in those families. Both type of results provide necessary and sufficient conditions for the quasi-polynomial families to be robustly stable independent of delay. Index Terms--Frequency-sweeping tests, robust stability, time-delay systems, uncertain quasi-polynomials, vertex tests.

In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems. Index Terms--Delay margin, matrix pencil, neutral delay systems, stability, time delay.

We consider in this paper a class of dual control problems where there exists a parameter uncertainty in the observation equation of the linear-quadratic Gaussian problem. An analytical active dual control law is derived by a variance minimization approach. The issue of how to determine an optimal degree of active learning is then addressed, thus achieving an optimality for this class of dual control problems. Index Terms--Dual control, dynamic programming, linear-quadratic Gaussian (LQG) control problem, stochastic control.