Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit

Robust Controller Design for Uncertain Lure Systems Guaranteeing Dichotomy Behaviors

“…From the above inequality we get (6) and the proof is completed. Remark 3.1 In [5], the frequency domain inequality is…”

“…We can see that each of the conditions obtained above is just one of the situations for τ or γ . Theorem 3.1 is obtained directly from Lemma 2.1, which is less conservative than the sufficient conditions in [5,6,8].…”

“…where A, C , D and ϕ are defined as in Section 2, 1 B is the same as B in system (1), u R ∈ is the control input and A ∆ , B ∆ satisfying (5 …”

“…The analysis and synthesis problem of such systems are much different from systems with single equilibrium. The nonlinear systems have various global behaviors such as Lagrange stability [2][3][4], dichotomy [5][6][7][8][9][10][11][12], gradient-like [13][14][15][16], Bakaev stability and so on.…”

“…A state feedback controller is designed to eliminate the chaotic phenomena by guaranteeing the chaos system dichotomy [5]. Gradient-like and dichotomy behaviors of pendulum-like dynamical networks systems are considered in [6].…”