State feedback \(L_1\)-gain control of positive 2-D continuous switched delayed systems via state-dependent switching. (English) Zbl 1346.93201
Summary: This paper investigates the stability and \(L_1\)-gain control of two-dimensional (2-D) continuous positive switched delayed systems. Firstly, by constructing an appropriate co-positive Lyapunov-Krasovskii functional, a sufficient condition for asymptotical stability of the system under consideration is derived. Secondly, \(L_1\)-gain performance analysis of the underlying system is investigated. Thirdly, a design methodology for state feedback controller is proposed to ensure that the closed-loop system is asymptotically stable with \(L_1\)-gain performance. Finally, an example is provided to show the effectiveness of the proposed method.
MSC:
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93B52 | Feedback control |
| 93D15 | Stabilization of systems by feedback |
Keywords:
positive systems; 2-D systems; switched systems; state feedback control; \(L_1\)-gain performance; time-varying delaySoftware:
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