Linear Matrix Inequalities in System and Control Theory¶
Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Convexity
- Decision theory and ethics. Utilitarian aggregation, mixed strategies, randomized policies, and veil-of-ignorance arguments all use convex combinations; the convex hull of pure options is the set of feasible compromises. Engineering and physics. Lyapunov functions are convex certificates of stability, and linear matrix inequalities reformulate controller synthesis as convex feasibility; thermodynamic free energy is convex in extensive variables, which underwrites phase boundaries via the convex-hull construction.
This sourceLyapunov functions as convex stability certificates and LMI reformulation of controller synthesis as convex feasibility.
- Decision theory and ethics. Utilitarian aggregation, mixed strategies, randomized policies, and veil-of-ignorance arguments all use convex combinations; the convex hull of pure options is the set of feasible compromises. Engineering and physics. Lyapunov functions are convex certificates of stability, and linear matrix inequalities reformulate controller synthesis as convex feasibility; thermodynamic free energy is convex in extensive variables, which underwrites phase boundaries via the convex-hull construction.
- Stability
- Lyapunov's 1892 framework moved from differential equations into all modern controller design — PID, LQR, MPC, robust and adaptive control — with the linear-matrix-inequality formulation as its operational form.
This sourceOperational LMI formulation of Lyapunov stability used across modern controller design.
- Lyapunov's 1892 framework moved from differential equations into all modern controller design — PID, LQR, MPC, robust and adaptive control — with the linear-matrix-inequality formulation as its operational form.
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