Bounded Integral Control of Input-to-State Practically Stable Nonlinear Systems to Guarantee Closed-Loop Stability

• Published in: IEEE transactions on automatic control Vol. 61; no. 12; pp. 4196 - 4202
• Main Authors: Konstantopoulos, G. C., Zhong, Q.-C, Ren, B., Krstic, M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic stability; Bounded input; Closed loop systems; Control stability; Control systems; Controllers; Feedback control; input-to-state stability; integral control; Integral equations; Integrated circuits; Nonlinear systems; Parameters; Power converters; small-gain theorem; Stability criteria; System theory; Systems stability; Systems theory
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2016.2552978

A fundamental problem in control systems theory is that stability is not always guaranteed for a closed-loop system even if the plant is open-loop stable. With the only knowledge of the input-to-state (practical) stability (ISpS) of the plant, in this note, a bounded integral controller (BIC) is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness. When a given bound is required for the control output, an analytic selection of the BIC parameters is proposed and its performance is investigated using Lyapunov methods, extending the result for locally ISpS plant systems. Additionally, it is shown that the BIC can replace the traditional integral controller (IC) and guarantee asymptotic stability of the desired equilibrium point under certain conditions, with a guaranteed bound for the solution of the closed-loop system. Simulation results of a DC/DC buck-boost power converter system are provided to compare the BIC with the IC operation.