L 1 Input-Output Finite-Time Control of Positive Switched Nonlinear Systems

Abstract EN

In this paper, the problem of L1 input-output finite-time control of positive switched nonlinear systems with time-varying and distributed delays is investigated.

Nonlinear functions considered in this paper are located in a sector field.

Firstly, the proof of the positivity of switched positive nonlinear systems with time-varying and distributed delays is given, and the concept of L1 input-output finite-time stability (L1 IO-FTS) is firstly introduced.

Then, by constructing multiple co-positive-type nonlinear Lyapunov functions and using the average dwell time (ADT) approach, a state feedback controller is designed and sufficient conditions are derived to guarantee the corresponding closed-loop system is L1 IO-FTS.

Such conditions can be easily solved by linear programming.

Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.