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Verification and synthesis of interconnected embedded control systems under timing contracts

In the first part of this paper, we solve the problem of verifying stability of an interconnection of embedded control systems under a timing contract which specifies the time instants at which some operations in each subsystem are performed such as sampling, actuation, or control input computation. In our approach, we reformulate each subsystem into an impulsive system and then derive a small gain condition on the stability of the interconnection using reachability analysis. In the second part of the paper, we consider the problem of synthesizing a set of timing contracts that guarantee the stability of the interconnected embedded control system by exploiting the monotonicity of stability with respect to timing contract parameters. Linear and nonlinear examples are provided allowing us to compare our results with existing techniques and to show the effectiveness of our approach.