In this paper, we study the boundary output feedback stabilization for an Orr-Sommerfeld equation cascaded by both the Squire equation and ordinary differential equations. The observer is proposed and the gain functions are found by the backstepping method. The observer-based controller is designed by using the certainty-equivalent principle. The existence and exponential stability of the closed-loop system are proved by calculating the system operator to generate a C0-semigroup and its eigenfunctions to form the Riesz basis approach.
|Number of pages||6|
|State||Published - 2022|
|Event||4th IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2022 - Kiel, Germany|
Duration: 7 Sep 2022 → 9 Sep 2022
- Orr-Sommerfeld equation
- Squire equation
- boundary control