Consensus of positive real systems cascaded with a single integrator

Abstract

SUMMARYWe study output consensus in a network of interconnected non-identical positive real systems cascaded with a single integrator. Assuming undirected, diffusive interconnections, sufficient conditions are provided to ensure output consensus for two cases: (i) the individual systems are weakly strictly positive real systems cascaded with a single integrator, and (ii) the individual systems are positive real systems cascaded with a single integrator. We illustrate our results with the example of a load frequency control network of synchronous generators.

Studies on Resilient Control Through Multiagent Consensus Networks Subject to Disturbances

“…Remark 5: From Theorem 2, we know that one can exactly obtain T yω ∞−2 through solving the Lyapunov equation (15). This is obviously different from the computation of T yω 2−2 , which is achieved by instead determining it with an appropriate upper bound.…”

“…Corollary 2: The following four conditions are equivalent: 1) there exists W 0 satisfying the Lyapunov equation (15); 2) there exists X 0 satisfying the Lyapunov inequality (16); 3) there exists X 0 satisfying the LMI (21); 4) G(A) has a spanning tree. Proof: To derive this corollary, we only need to prove the equivalence between 1) and 4).…”

“…Lemma 4: There exists a positive definite matrix 0 ≺ W ∈ R (n−1)×(n−1) satisfying the Lyapunov equation (15) if and only if there exists a positive definite matrix 0 ≺ X ∈ R (n−1)×(n−1) satisfying the following Lyapunov inequality:…”

“…With the above development, we know that three equivalent conditions, i.e., (15), (16), and (21), are provided to accomplish T yω ∞−2 , to quantitatively assess the system resilience for multiagent consensus networks in the face of disturbances belonging to L 2 . For the three conditions, we can also establish a network topology condition associated with G(A) to provide them a necessary and sufficient guarantee.…”

“…To motivate our approach we first note that a number of physically relevant systems exist that admit system dynamics that can be modeled as a consensus network. One such physical system is the power system [2], [3], [15]. Another example is the model of thermal processes in a building [16].…”