Control Design for Switched Affine Systems
Summary
Switched affine systems comprise a family of affine subsystems—each defined by linear dynamics with an additive constant term—together with a rule that governs transitions between them. These systems arise naturally in applications such as power electronics, automotive control, robotics and networked systems, where abrupt changes in operating conditions or control objectives demand dynamic reconfiguration. The control design problem centres on the synthesis of switching laws and continuous inputs that ensure stability, performance and robustness irrespective of the active mode or sequence of mode transitions. Key challenges include the accommodation of mode-dependent equilibria, the management of transient behaviour at switching instants, and the maintenance of guaranteed performance levels under uncertainty or disturbances. Modern approaches exploit multiple Lyapunov functions and piecewise-quadratic Lyapunov functions to derive tractable conditions in the form of linear matrix inequalities (LMIs). Advanced techniques further integrate dwell-time constraints to limit the frequency of switching, convex-combination methods to handle constant offsets, and hybrid optimisation to balance complexity against real-time implementation. As a result, the field has seen steady progress towards controllers that are not only provably stable and performant, but also amenable to efficient numerical synthesis and validation.
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Control Design for Switched Affine Systems publication trend
The graph below shows the total number of articles in control design for switched affine systems across all publications each year (not limited to Nature Index journals).
Technical terms
Switched affine system: A dynamical system that switches among multiple affine subsystems, each described by linear dynamics plus a constant term, according to a switching signal.
Lyapunov function: A scalar function that decreases along system trajectories and is used to certify stability of equilibrium points.
Dwell time: A constraint imposing a minimum duration between consecutive switches to avoid excessive chattering and to facilitate stability analysis.
Linear matrix inequality (LMI): A convex constraint on matrix variables that can be efficiently solved to verify stability and performance conditions.
Domain of attraction: The set of initial states from which the closed-loop system converges to a desired equilibrium under the prescribed control law.
References
- Local stabilization conditions for discrete-time switched affine systems. Automatica (2024).
- Stability of switched systems with multiple equilibria: A mixed stable–unstable subsystem case. Systems & Control Letters (2023).
- A note on quadratic performance of a class of switched uncertain nonlinear systems. Systems Science & Control Engineering (2024).
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