Universal formula for robust stabilization of affine nonlinear multistable systems

Design of Controls for Boundedness of Trajectories of Multistable State Periodic Systems

“…Moreover, the controller (12) vanishes at every element of the set U since by definition b(0) ≡ 0. Therefore, U is contained in the equilibrium set of the closed-loop system (4), (12). Finally, we are able to establish the following results.…”

“…Theorem 2: Let the system (4) satisfy Assumption 2. If there exists a CLeF as in Definition 2 satisfying the SCP-LeF (10), then the periodic feedback control law ( 12) is continuous on R n , and for all x 0 ∈ R n the trajectories X(t, x 0 ) of the closed-loop system (4), (12) are bounded for all t ≥ 0.…”

“…, then the feedback control law ( 12) is continuous on R n , and for all x 0 ∈ R n the trajectories X(t, x 0 ) of the closed-loop system (4), (12) are bounded for all t ≥ 0. Corollary 2 is a counterpart of Corollary 1 that relaxes the conditions of Definition 1.…”

“…However, the study of stability and boundedness of solutions for multistable systems requires significant modifications and relaxations of the employed Lyapunov stability notions, see for example [5]- [11]. In this context, extensions of the control Lyapunov function framework for multistable systems have been presented in [12], [13].…”