Stabilization of two coupled wave equations with joint anti-damping and non-collocated control

Boundary tracking control of an unstable cascaded heat system with a non‐collocated feedback

“…In reference [8], the backstepping method also is applied to study the inputto-state stabilization of an ODE-heat cascade system with disturbances. Different from the backstepping method, in our recent works [9][10][11][12], the unstable PDE systems are stabilized by using the non-collocated control through the finite dimensional compensator or the proportional boundary feedback.…”

“…A feasible method is the backstepping method (see references [4] and [7]) to stabilize the unstable system by designing the state feedback control, which needs each point of the system state to be measurable and is not easy to implement in practical engineering. Motivated by our recent works [9][10][11][12], we propose a simple non-collocated static feedback control to stabilize the error system, which is easy to be applied in practical engineering because of its simple structure. To overcome the difficulty of the lack of dissipativity caused by the non-collocated feedback, we apply the Nyquist criterion to discuss the position of the system's spectrum and give the admissible feedback gain through a rigorous mathematical derivation.…”