This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

We study the local exponential stabilization of the 2D and 3DNavier-Stokes equations in a bounded domain, around a givensteady-state flow, by means of a boundary control. We look for acontrol so that the solution to the Navier-Stokes equations be astrong solution. In the 3D case, such solutions may exist if theDirichlet control satisfies a compatibility condition with theinitial condition. In order to determine a feedback law satisfyingsuch a compatibility condition, we consider an extended systemcoupling the Navier-Stokes equations with an equation satisfied bythe control on the boundary of the domain. We determine a linearfeedback law by solving a linear quadratic control problem for thelinearized extended system. We show that this feedback law alsostabilizes the nonlinear extended system.

For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying periodic feedback.

This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V 0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration.

This paper deals with the problem of stabilizing a system in the presence ofsmall measurement errors. It is known that, for general stabilizable systems,there may be no possible memoryless state feedback which is robust withrespect to such errors. In contrast, a precise result is given here, showingthat, if a (continuous-time, finite-dimensional) system is stabilizable in anyway whatsoever (even by means of a dynamic, time varying, discontinuous,feedback) then it can also be semiglobally and practicallystabilized in a way which is insensitive tosmall measurement errors, by means of a hybrid strategy based on the idea ofsampling at a “slow enough” rate.