LMIs in Control/pages/Algebraic Riccati Inequality
Algebraic Riccati Equations are particularly significant in Optimal Control, filtering and estimation problems. The need to solve such equations is common in the analysis and linear quadratic Gaussian control along with general Control problems. In one form or the other, Riccati Equations play significant roles in optimal control of multivariable and large-scale systems, scattering theory, estimation, and detection processes. In addition, closed forms solution of Riccati Equations are intractable for two reasons namely; one, they are nonlinear and two, are in matrix forms.
The System[edit | edit source]
The Data[edit | edit source]
Following matrices are needed as Inputs:.
The Optimization Problem[edit | edit source]
In control systems theory, many analysis and design problems are closely related to Riccati algebraic equations or inequalities. Find
The LMI: Algebraic Riccati Inequality[edit | edit source]
Title and mathematical description of the LMI formulation.
Conclusion:[edit | edit source]
If the solution exists, LMIs give a unique, stabilizing, symmetric matrix P.
Implementation:[edit | edit source]
Matlab code for this LMI in the Github repository:
- REDIRECT []