The work that follows is a continuation of the investigation of metric based nonlinear state transformations, but with applications to observers for plants with measurement uncertainty. In particular, these transformations are shown to be useful for linear and stable systems, and appear to be highly effective when sensor bias is present. It turns out that a nonlinear observer can be constructed based upon the existing Luenberger linear structure, i.e., Kalman filter. This nonlinear structure enables the estimated state construction to become less sensitive to sensor uncertainty due to the transformation itself. Although the plant realizations in this note are assumed stable and linear, the uncertainty comes from the measurement noise (as a bounded but unknown bias). Examples are provided that suggests this nonlinear observer has promising characteristics, and in particular robustness to state estimate error when the measurements are contaminated with bias uncertainty.

 Explicit tuning rules for digital PID regulators are presented regarding the control of integrating processes. Controller parameters are determined analytically as a function of the process parameters and the sampling time of the controller. The derivation of the proposed PID control law lies in the principle of the Symmetrical Optimum criterion. The performance of the proposed control law is compared with the conventional tuning of the PID regulator via the Symmetrical Optimum criterion when controlling the same process. Simulation examples show improvement of output disturbance rejection of up to 71.05% decrease of settling time.

 This note studies the problem of bounds for the Lyapunov exponent of a parameter perturbed system when the perturbation has finite average value. Such a bound is presented in terms of Bohl exponent of the unperturbed system. In particular, it has been shown that the Lyapunov exponent of perturbed system is not greater than the Bohl exponent of the unperturbed system if the average value of perturbations is zero. The obtained result is illustrated by a numeri4cal example.

 Errors-in-variables system identification can be posed and solved as a Hankel structured low-rank approximation problem. In this paper different estimates based on suboptimal low-rank approximations are proposed. The estimates are shown to have almost the same efficiency and lead to the same minimum when supplied as an initial approximation for local optimization in the structured low-rank approximation problem. In this paper it is shown that increasing Hankel matrix window length improves initial approximation for autonomous systems and does not improve it in general for systems with inputs.

 An innovative method for robust stabilizing PI,PD controller design and its stabilizing area approximation is presented for discrete-time SISO plants. It starts from the random generation of Schur stable polynomials using reflection coefficients and reflection segments of polynomials. Stable reflection segments are projected onto affine set of closed-loop characteristic polynomials which is defined by the controller parameters and the stable line segments in the controller parameter space are then determined. The segments of two systems with different parameters are used to generate a rectangular and polygonal approximations of the stabilizing area of robust controller parameters that stabilize both systems.