## Universal stabilization of feedforward nonlinear systems.(English)Zbl 1010.93080

The author considers the following class of locally Lipschitz feedforward nonlinear systems \begin{aligned} &\dot x_1 = x_2+\varphi_1(x_3,\dots,x_n,u),\\ &\dot x_2 = x_3+\varphi_2(x_4,\dots,x_n,u),\\ &\vdots\\ &\dot x_{n-1} = x_n+\varphi_{n-1}(u),\\ &\dot x_n = u, \end{aligned}\tag{1} where $$x=[x_1,\dots,x_n]^T\in\mathbb{R}^n$$ is the state, $$u\in\mathbb{R}$$ is the control and $$\varphi_i$$ are unknown functions vanishing at zero. The distinguished feature of this paper is that the design of a global stabilizer does not require a priori information on the functions $$\varphi_i$$.

### MSC:

 93D15 Stabilization of systems by feedback 93C10 Nonlinear systems in control theory
Full Text:

### References:

 [1] Fu, M.; Barmish, B.R., Adaptive stabilization of linear systems via switching control, IEEE transactions on automatic control, 31, 1097-1103, (1986) · Zbl 0607.93041 [2] Jankovic, M.; Sepulchre, R.; Kokotovic, P.V., Constructive Lyapunov stabilization for feedforward systems, IEEE transactions on automatic control, 41, 1723-1735, (1996) · Zbl 0869.93039 [3] Jankovic, M.; Sepulchre, R.; Kokotovic, P.V., Global adaptive stabilization of cascade nonlinear systems, Automatica, 33, 263-268, (1997) · Zbl 0876.93082 [4] Khalil, H.K.; Saberi, A., Adaptive stabilization of a class of nonlinear systems using high-gain feedback, IEEE transactions on automatic control, 32, 1031-1035, (1987) · Zbl 0625.93040 [5] Lin, W., & Qian, C. (1998). New results on global stabilization of feedforward systems via small feedback. Proceedings of the IEEE CDC, Tampa, USA, pp. 873-878. [6] Mazenc, F.; Praly, L., Adding integrations, saturated controls, and stabilization for feedforward systems, IEEE transactions on automatic control, 41, 1559-1578, (1996) · Zbl 0865.93049 [7] Miller, D.E.; Davison, E.J., An adaptive controller which provides an arbitrary good transient and steady-state response, IEEE transactions on automatic control, 36, 68-81, (1991) · Zbl 0725.93074 [8] Morse, A.S. (1995). Control using logic-based switching. In: A. Isidori (Ed.), Trends in control (pp. 69-113) New York, Springer. [9] Qian, C., & Lin, W. (1999). Using small feedback to stabilize a wider class of feedforward systems. Proceedings of the IFAC World Congress, Vol. E, Beijing, China, pp. 309-314. [10] Sepulchre, R.; Jankovic, M.; Kokotovic, P.V., Integrator forwardinga new recursive nonlinear robust design, Automatica, 33, 979-984, (1997) · Zbl 0881.93066 [11] Teel, A. R. (1992). Using saturation to stabilize a class of single-input partially linear composite systems. Proceedings of the IFAC NOLCOS, Bordeaux, France, pp. 379-384. [12] Teel, A.R., A nonlinear small gain theorem for the analysis of control systems with saturation, IEEE transactions on automatic control, 41, 1256-1270, (1996) · Zbl 0863.93073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.