Abstract—We consider the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set

information. Our loop invariant synthesis is conducted automatically by a fixpoint iteration process, equipped with newly designed abstraction mechanism, and join and widening operators. Initial experiments have confirmed that we can synthesise loop invariants with non-trivial constraints.

We present a technique for refining incorrect or insufficiently strong loop invariants in correctness proofs for imperative programs. We rely on previous work [16] in combining program analysis and Proof Planning, and exploit IsaPlanner’s use of meta-variables and goal-naming to generate correct

on users to supply annotations to guide the verification, which can be cumbersome and error-prone by hand and can significantly restrict the usability of the verification system. In this paper, we reduce the need for some user annotations by automatically inferring loop invariants over an abstract domain

Abstract. Usually, ranking function synthesis and invariant generation over a loop with integer variables involves abstracting the loop to have real variables. Integer division and modulo arithmetic must be soundly abstracted away so that the analysis over the abstracted loop is sound

Abstract. We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with linear guards and transitions. Proving termination via linear ranking functions often requires invariants; yet invariant generation is expensive

Abstract. Among the various critical systems that worth to be for-mally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com-putations update internal states and produce commands to update the system state. Those

Abstract For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly

Computing invariants is the key issue in the analysis of infinite-state systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied

termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions consisting of polynomial assertions, including inequalities, over primed and unprimed variables. Next, we address synthesis of these functions with a complete and automatic method