This paper studies stabilization of uncertain systems over finite data rate and lossy channels. Limitations on data rate and packet loss probability are derived, characterized by the product of the eigenvalues of the plant. It is worth noting that even if we assume the most conservative plant dynamics, existing limitations for nominal plants are looser than those given in this paper. This fact implies that plant uncertainties cause strictly higher requirements in communication. We consider linear discrete-time systems with parametric uncertainties and employ uniform quantizers, which have the simplest quantization structure. Under the setup, a necessary condition and a sufficient condition for stability are derived. In particular, for scalar plants case, the conditions are exact. They coincide with the existing results for nominal plants as a special case and hence generalize them to the uncertain case.

The purpose of the paper is to show that boundary implication results hold for complex-valued uncertain linear time-delay systems. The results are derived by the Lambert W function and yield tractable robust stability criteria for simultaneously triangularizable linear time-delay systems. The setting is similar to a recently reported extreme-point result, but the assumed uncertainty sets can be much more free in shape.

This letter presents parametric uncertainty bounds (PUBs) for stabilizing receding horizon H∞ control (RHHC). The proposed PUBs are obtained easily by solving convex optimization problems represented by linear matrix inequalities (LMIs). We show, by numerical example, that the RHHC can guarantee a H∞ norm bound for a larger class of uncertain systems than conventional infinite horizon H∞ control (IHHC).

This letter presents robustness bounds (RBs) for receding horizon controls (RHCs) of uncertain systems. The proposed RBs are obtained easily by solving convex problems represented by linear matrix inequalities (LMIs). We show, by numerical examples, that the RHCs can guarantee robust stabilization for a larger class of uncertain systems than conventional linear quadratic regulators (LQRs).

A novel digital redesign methodology based on evolutionary programming (EP) is introduced to find the 'best' digital controller for optimal tracking design of hybrid uncertain multi-input/ multi-output (MIMO) input-delay systems with constraints on states and controls. To deal with these multivariable concurrent specifications and system restrictions, instead of conventional interval methods, the proposed global optimization scheme is able to practically implement optimal digital controller for constrained uncertain hybrid systems with input time delay. Further, an illustrative example is included to demonstrate the efficiency of the proposed method.

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of an upper bound on the worst-case infinite horizon cost function at each time instant. It is shown that the mean square stability of the proposed control system is guaranteed under some matrix inequality conditions on the terminal weighting matrices. The proposed controller is obtained using semidefinite programming.

Data of system parameters of real systems have some uncertainty and they should be given by sets (or intervals) rather than fixed values. To analyze and design systems contaning such uncertain parameters, it is required to represent and treat uncertainty in data of parameters, and to compute value sets of characteristic polynomials and transfer functions. Interval arithmetic is one of the most powerful tools to perform such subjects. In this paper, Polygon Interval Arithmetic (PIA) on the set of polygons in the complex plane is considered, and the data structure and algorithms to execute PIA efficiently is proposed. Moreover, practical examples are shown to demonstrate how PIA is useful to compute the evaluation of value sets.