Robust performance synthesis for systems with positive-real uncertainty and an extension to the negative-imaginary case

Distributed robust stabilization of networked multiagent systems with strict negative imaginary uncertainties

“…Using phase information in control design for lightly damped (ie, highly resonant) systems is much more effective than using gain information. 18,19 In other words, for such lightly damped systems gain stabilization, which is dependent on the small-gain theorem, leads to conservative design results. 11,18 On the other hand, phase stabilization, which ensures stability by restricting the phase of the open-loop system and by which the NI robust stability results were established, yields more powerful, less conservative, and robust control systems.…”

“…11,18 On the other hand, phase stabilization, which ensures stability by restricting the phase of the open-loop system and by which the NI robust stability results were established, yields more powerful, less conservative, and robust control systems. 19,20 Thus, it is of interest to investigate how distributed control protocols can be designed to stabilize networked multiagent systems with SNI uncertainties via the NI systems theory. Although the work of Wang et al, 9 which studied robust cooperative control of multiple NI systems, took into account SNI uncertainties, the nominal plants were assumed to be NI.…”

“…Robust synchronization of uncertain multiagent networks was addressed in the works of Trentelman et al and Jongsma et al with uncertainties in the form of additive perturbations in the work of Trentelman et al and in the form of coprime factor perturbations in the work of Jongsma et al Robust consensus control for multiagent systems involving gap metric uncertainties was investigated in the work of Alvergue et al It is known that the dynamic uncertainties of NI systems are mainly characterised by phase bounds, where the phase lies between − π and 0. Using phase information in control design for lightly damped (ie, highly resonant) systems is much more effective than using gain information . In other words, for such lightly damped systems gain stabilization, which is dependent on the small‐gain theorem, leads to conservative design results .…”

“…In other words, for such lightly damped systems gain stabilization, which is dependent on the small‐gain theorem, leads to conservative design results . On the other hand, phase stabilization, which ensures stability by restricting the phase of the open‐loop system and by which the NI robust stability results were established, yields more powerful, less conservative, and robust control systems . Thus, it is of interest to investigate how distributed control protocols can be designed to stabilize networked multiagent systems with SNI uncertainties via the NI systems theory.…”

Controller Synthesis to Render a Closed Loop Transfer Function Strongly Strictly Negative Imaginary

“…In fact, there exists a transformation from the former to the latter by means of a blocking zero at the origin [1]. However, this transformation has complicated the use of existing solutions of the PR synthesis problem [6], [7], [8], [9], [10], [11] to solve the corresponding NI problem. This is because WSNI systems are transformed into non-strict PR systems and not WSPR systems [1], [12].…”