L₁/ℓ₁-to-L₁/ℓ₁ analysis of linear positive impulsive systems with application to the L₁/ℓ₁-to-L₁/ℓ₁ interval observation of linear impulsive and switched systems

2018/01/10 by Briat, Corentin
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1801.03789

Abstract

Sufficient conditions characterizing the asymptotic stability and the hybrid L₁/ℓ₁-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. These conditions are then adapted to formulate constructive and convex sufficient conditions for the existence of L₁/ℓ₁-to-L₁/ℓ₁ interval observers for linear impulsive and switched systems. Suitable observer gains can be extracted from the (suboptimal) solution of the infinite-dimensional optimization problem where the L₁/ℓ₁-gain of the system mapping the disturbances to the weighted observation errors is minimized. Some examples on impulsive and switched systems are given for illustration.

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