Equilibrium Points of Second-Order Linear Systems with Single Saturated Input
This chapter is dedicated to presenting equilibrium points for second-order differential systems with single saturated input. The focus of this chapter is on the so-called 0–1 algebra-geometry type structure equations and their equilibrium points under many cases. The chapter attempts to provide constructive qualitative methods on equilibrium points for second-order linear systems with saturated inputs. By defining new equilibrium points, the relationship between equilibrium points is discussed for second-order linear systems with a single saturated input. Moreover, many interesting examples, including their corresponding stability and possible limited cycles, are effectively shown to illustrate the above results.
This work is Supported by National Key Research and Development Program of China (2017YFF0207400).
- 4.Huang L. Stability theory. Beijing: Peking University Press; 1992. p. 235–83.Google Scholar
- 14.Sontag ED, Sussmann HJ. Nonlinear output feedback design for linear systems with saturated control. In: Proceeding of 29th conference on decision and control, vol. 45(5);1990. p. 719–721.Google Scholar
- 16.Tarbouriech S, Gomes da JM. Synthesis of controllers for continuous-times delay systems with saturated control via LMIs. IEEE Trans Autom Control. 2000;45(1):105–11.Google Scholar