\(L_1\)-gain analysis and control synthesis of positive switched systems. (English) Zbl 1332.93127
Summary: This paper investigates the problems of \(L_1\)-gain analysis and control synthesis of positive switched systems. Linear supply rates and \(L_1\)-gain notations are introduced to analyse the performance of the underlying systems. Stability with a weighted \(L_1\)-gain for autonomous systems are solved by using multiple linear copositive Lyapunov functions incorporated with the average dwell time approach. Then, state-feedback and output-feedback controllers are designed to guarantee the stabilisation with a weighted \(L_1\)-gain for non-autonomous systems. All present conditions are solvable in terms of linear programming. Finally, a practical example is given to illustrate the validity of theoretical findings.
MSC:
| 93B50 | Synthesis problems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 90C05 | Linear programming |
| 93B52 | Feedback control |
Keywords:
positive switched systems; multiple linear co-positive Lyapunov functions; linear programming; state-feedback controller; output-feedback controllerReferences:
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