Stability Of Nonlinear Sampled-data Systems Research Articles

On the stability of nonlinear sampled-data systems and their continuous-time limits

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between specific stability properties of the exact discrete-time model and stability properties of the continuous-time system that is obtained when the maximum admissible sampling period tends to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the closed-loop sampled-data system. Compared to the literature, our results allow to prove stronger (asymptotic) sampled-data stability properties for nonlinear systems in cases for which existing results only guarantee practical stability.

Further results on sampled-data stabilization of time-delay systems

The paper deals with the stabilization of nonlinear sampled-data systems affected by non-entire input-delays. The approach combines input-Lyapunov matching, prediction and Immersion and Invariance concepts. The result is also detailed for linear dynamics and illustrated on a benchmark example.

Input-to-state stabilization for nonlinear dual-rate sampled-data systems via approximate discrete-time model

The problem of state feedback stabilization of nonlinear sampled-data systems is considered under the “low measurement rate” constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. Given an approximate discrete-time model of a sampled nonlinear plant and given a family of controllers that stabilizes the plant model in input-to-state sense, we show that under some standard assumptions the closed loop dual-rate sampled data system is input-to-state stable in the semiglobal practical sense.

A Framework for Stabilization of Nonlinear Sampled-Data Systems Based on Their Approximate Discrete-Time Models

A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.

Popov-Type Criterion for Stability of Nonlinear Sampled-Data Systems

This paper studies input/output stability of nonlinear sampled-data systems with a sector nonlinearity. A stability condition of circle-criterion type was derived recently, for the case where the sector nonlinearity is possibly time varying and dynamical. In contrast, this paper deals with the case where it is time invariant and memoryless, and gives a less conservative stability criterion for such a case. It is derived by applying the multiplier technique, and corresponds to the Popov criterion in the continuous-time setting. The arguments make use of the frequency-domain theory of sampled-data systems, and a sort of convexity in the frequency domain plays an important role. A method with the cutting-plane algorithm is provided for finding a multiplier that proves stability. An illustrative example is also given.

Slow sampling and stability of non-linear sampled-data systems

The stabilization of a class of sampled-data systems by slow sampling is studied. A relationship is obtained between the minimum sampling period and an estimated domain of attraction of the system.

Nonlinear-discrete data systems extension of the known sector of stability

A simple and elegant method for widening the domain of stability of nonlinear sampled-data systems to an appreciable extent is presented. The order of the difference equation is artificially increased in order to examine the behavior of the system in the time domain for a longer duration than indicated by the dynamics of the system. The utility of some of the well-known methods can be considerably enhanced by the technique described here. The method is illustrated by several examples, some of which are difficult to solve by the existing methods.

Frequency criteria for bounded-input--Bounded-output stability of nonlinear sampled-data systems

Sufficient conditions for absolute stability in the bounded-input-bounded-output sense are obtained for a class of nonlinear sampled-data systems. The criteria are identical to those establishing absolute stability in a global stability sense for the same class of autonomous nonlinear sampled-data systems.

Stability of nonlinear sampled-data systems with finite sampling duration

Stability of nonlinear sampled-data systems with finite sampling duration