Finite-Time Control Strategies for Linear and Nonlinear Systems
Summary
Finite-time control refers to the design and analysis of feedback mechanisms that drive a dynamical system’s state to a desired condition within a predetermined, finite interval. This contrasts with traditional asymptotic control, which guarantees convergence only as time tends towards infinity. In linear settings, finite-time approaches exploit linear matrix inequalities and specially constructed Lyapunov–Krasovskii functionals to obtain explicit settling-time bounds and robustness against time-varying delays or uncertainties. In nonlinear systems, techniques such as backstepping, sliding mode control and barrier-function methods have been adapted to enforce finite-time convergence while handling non-smooth dynamics and external disturbances. The finite-time paradigm has gained traction due to its ability to ensure rapid response, enhance disturbance rejection and guarantee performance within strict time constraints. Applications span electric power grids, robotic manipulators, aerospace systems and networked control, where the assured completion of critical tasks in bounded time is essential. Recent advances have also integrated stochastic frameworks, event-triggered schemes and hybrid structures to further tighten settling-time guarantees and reduce computational burden. Overall, finite-time control strategies offer a robust and versatile toolkit for the precise regulation of both linear and nonlinear processes under practical constraints.
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Finite-Time Control Strategies for Linear and Nonlinear Systems publication trend
The graph below shows the total number of articles in finite-time control strategies for linear and nonlinear systems across all publications each year (not limited to Nature Index journals).
Technical terms
Finite-time stability: Property ensuring system states reach a desired equilibrium within a fixed time bound rather than asymptotically.
Lyapunov–Krasovskii functional: A generalisation of Lyapunov functions accommodating systems with delays by incorporating integral terms to assess stability.
Linear matrix inequality (LMI): A convex constraint on matrix variables commonly used to derive tractable conditions for controller synthesis.
Sliding mode control: A robust strategy that forces system trajectories onto a designated switching surface, achieving finite-time convergence and disturbance rejection.
References
- Input-Output Finite-Time Sliding Mode Control of Discrete Time-Varying Systems Under an Adaptive Event-Triggered Mechanism. IEEE Access (2023).
- Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays. Mathematics (2022).
- Robust Finite-Time Control of Linear System with Non-Differentiable Time-Varying Delay. Symmetry (2020).
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