On the solvability of the constrained Lyapunov problem

Abstract

This paper considers system theoretic conditions for the solvability of the so-called Constrained Lyapunov Problem for non-square systems. These problems commonly appear in the control systems literature. Both a static output feedback problem and an observer problem are considered. The basis for the work described here is a new canonical form which simplifies the analysis and deals with the equality constraint in a simple way.

LPV sliding mode observers for sensor fault reconstruction with erroneous scheduling parameter measurements

“…Using ideas similar to those in [15], for a sufficiently large positive k, the matrix P = diag(P 1 , I p ) has the property that…”

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“…Sometimes this reduced order problem is more amenable to solution: for example, if the matrix triple is related to a one input and two outputs system, the output feedback problem reduces to a classical "root-locus" investigation [2]. Remark 2.…”

“…Consider the time-delay interconnected system (1)-(2). Under Assumptions 1-4, there exists a global delay dependent static output feedback decentralised control law which drives the system (1)-(2) to the composite sliding surface (16)-(17) and maintains a sliding motion on it thereafter.…”

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