Sampled-Data Control Systems Analysis and Optimization

Sampled‐data control systems address the interplay between continuous‐time plant dynamics and discrete‐time control interventions. By employing devices such as a zero‐order hold, digital controllers update inputs at fixed intervals while the process evolves continuously. Analysis and optimisation hinge on closed‐loop stability, disturbance rejection, robustness to model uncertainty and precise trajectory tracking. Central performance measures include the H∞ norm for worst‐case disturbance attenuation, the H2 norm for energy‐based criteria and induced or Hankel norms to quantify hybrid input‐to‐output gains. Modern advances leverage hybrid‐systems theory, variational principles on arbitrary time scales and linear matrix inequalities to reconcile continuous and discrete specifications. Computational techniques such as piecewise polynomial and superellipsoidal approximations provide tight error bounds and tractable solutions. Applications span robotic manipulators, networked control infrastructures, aerospace guidance and industrial automation, where sampling constraints, time‐varying delays and multirate schemes are intrinsic. By uniting theoretical insights with algorithmic innovation, sampled‐data control research continues to enhance the reliability and performance of digitally implemented control systems.

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Sampled-Data Control Systems Analysis and Optimization publication trend

The graph below shows the total number of articles in sampled-data control systems analysis and optimization across all publications each year (not limited to Nature Index journals).

Technical terms

Sampling period (h): The constant interval between successive measurements or control updates in a digital control scheme.

Zero‐order hold (ZOH): A device that converts discrete control values into a piecewise‐constant continuous signal over each sampling interval.

H∞ norm: A measure of the maximum gain from disturbance to output across all frequencies, indicating worst‐case robustness.

Hankel norm: The supremum of the norms of the Hankel operator evaluated over all phase shifts within the sampling period, reflecting energy transfer from past inputs to future outputs.

References

1. Optimal sampled-data control, and generalizations on time scales. Mathematical Control and Related Fields (2016).
2. $ L_2/L_1 $ induced norm and Hankel norm analysis in sampled-data systems. AIMS Mathematics (2024).
3. H ∞ and H 2 optimal sampled-data controller synthesis: A hybrid systems approach with mixed discrete/continuous specifications. Automatica (2021).
4. The $ l_\infty $-induced norm of multivariable discrete-time linear systems: Upper and lower bounds with convergence rate analysis. AIMS Mathematics (2023).
5. Computing the L∞-Induced Norm of LTI Systems: Generalization of Piecewise Quadratic and Cubic Approximations. IEEE Access (2020).
6. Construction of the Time-Optimal Bounded Control for Linear Discrete-Time Systems Based on the Method of Superellipsoidal Approximation. Автоматика и телемеханика (2023).