Ellipsoidal Sets for Static Output Feedback

Abstract

The static output feedback synthesis for LTI systems is considered. It is shown to have analogies with robust analysis, in particular the existence of an output feedback gain is equivalent to the existence of some quadratic separator. These considerations lead to formulate the problem as the synthesis of an ellipsoidal set of stabilising controllers. Based on this formulation important issues are developed for fragility, restricted controllers and also root-clustering.

LMI results for resilient state-feedback with H/sub /spl infin// performance

“…Hence, the set of uncertainties (12) is proved to be a sub-set of (11). Due to corollary 1, the LMI constraints (6) prove that K o is quadratically resilient to uncertainties such that (11).…”

“…The volume, defined in [12], could be a reference to compare controller sets and appreciate respective resilience. Unfortunately, volume does not take the geometry into account.…”

“…The approach of the present work is derived from results in [12], [9], [10]. Controller design is related to the framework of topological separation [13].…”

Output-feedback H<inf>&#x221E;</inf> control of a class of networked fault tolerant control systems

“…( [31,32]) Given three matrices X ∈ S q , Y ∈ R q×r and Z ∈ S r , the {X, Y, Z}-ellipsoid of R r ×q is the set of matrices K satisfying the following matrix inequalities:…”

Stabilizing Interconnection Characterization for Multi-Agent Systems with Dissipative Properties

“…a solution H satisfying (7) exist, if and only if the radiusR ≥ 0 is positive semidefinite, see e.g. Peaucelle et al [2002], being equivalent with requiring S 2 − RQ ≥ 0. This is always true as Q ≤ 0 and R ≥ 0.…”