Hybrid \(L_1\times\ell_1\)-gain performance analysis and synthesis of hybrid positive systems. (English) Zbl 1529.93083
Summary: This paper addresses the analysis and synthesis of hybrid positive systems with hybrid \(L_1\times\ell_1\)-gain performance. The considered systems contain both continuous- and discrete-time positive subsystems. The notion of hybrid \(L_1\times\ell_1\)-gain performance is introduced for hybrid positive systems. First, some sufficient conditions for the stability of the system without disturbances are established using a hybrid copositive Lyapunov function incorporated with average dwell time switching. Then, the characterization on the stability with hybrid \(L_1\times\ell_1\)-gain performance of the system with continuous- and discrete-time disturbances is explored based on linear programming. A hybrid average dwell time switching law is proposed, where continuous- and discrete-time subsystems have their own average dwell time switching. Furthermore, a hybrid controller of the system is designed by virtue of matrix decomposition approach. Finally, one example is given to verify the validity of the results.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C28 | Positive control/observation systems |
| 90C05 | Linear programming |
Keywords:
hybrid positive systems; hybrid gain performance; hybrid average dwell time switching; linear programmingReferences:
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