The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical ... |
If A is stable, there exists a quadratic Lyapunov function V (z) = zT Pz that proves it, i.e., there exists P > 0, Q > 0 that satisfies the (continuous- or ... |
The following method, proposed by Bartels and Stewart (1972), is now widely used as an effective computational method for the Lyapunov equation. |
Solving the Lyapunov equation. A. T. P + PA + Q = 0 we are given A and Q and want to find P if Lyapunov equation is solved as a set of n(n + 1)/2 equations in. |
Use lyap to solve the special and general forms of the Lyapunov equation. Lyapunov equations arise in several areas of control, including stability theory. |
The Lyapunov equation is the most com- mon problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation,. |
5 сент. 2012 г. · All Lyapunov equations AX+XAT=B have a unique, symmetric solution X=XT, unless there is a λ∈C such that λ and −λ are both eigenvalues of A. This ... |
Lyapunov functions have lead to one of the most important tools in the design and analysis of control systems, the Lyapunov equations. |
3 янв. 2022 г. · Abstract:The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and ... |
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