Analysis of linear parameter‐varying systems using a non‐smooth dissipative systems framework

Abstract

SUMMARYThis paper presents new finite-dimensional linear matrix inequality formulations for several important analysis problems of linear parameter-varying systems. The approach is based on a non-smooth dissipative systems framework using a continuous, piecewise-affine parameter-dependent Lyapunov function. The new analysis approach yields guaranteed and less conservative results than previously published techniques that are based on affine parameter-dependent Lyapunov functions or Lur! e e-Postnikov Lyapunov functions. Conservatism is reduced in this new approach because the analysis uses a more general class of parameterdependent Lyapunov functions (PDLFs). The new approach also provides an explicit trade-off between conservatism and computational effort of the analysis technique. Note that, in contrast to the gridding approach typically used to develop a computationally feasible algorithm, this proposed approach guarantees the analysis results. This paper also shows that the numerical results of our approach, while computationally intensive, could be used to develop many new insights into the selection of PDLFs in the other analysis techniques.

Quaternion Controller Design Using Switched Linear Parameter-Varying Framework

“…Note that the parameter µ is generally piecewise smooth and, thus, is different from the counterpart of SLPV systems. 3 However, Lim and Chan 4 recently showed that this difference has no effect on the SLPV analysis and synthesis. Also, note that each A i .µ/ is an af ne matrix function of µ (Ref.…”

“…3 First, Eq. (2) is conservatively modeled into a quasi-SLPV system with three assumptions: 1) the x of A.x/ is the parameter µ that is independentof the state x, 2) the unit-normquaternion constraint is ignored (which implies ¡1 · q k D 1;:::;4 · 1), and 3) the angular velocity !…”

“…These K i .µ/ can be found by the SLPV dissipation approach with quadratic storage function. 3 First, we derive a stability condition of the closed-loop SLPV system: The locally Lipschitz trajectories of the closed-loop SLPV system are uniformly stable if there exists a positive matrix P such that for i D 1; 2,…”

“…2 This Note proposesa new techniqueof designingquaternionfeedback controllers to facilitate fuel-ef cient eigenaxis rotations with a switched linear parameter-varying(SLPV) dissipation framework. 3 The spacecraft dynamics are rst formulated into an SLPV system. A stabilizing feedback controller for this SLPV spacecraft model is then derived by the SLPV dissipation approach.…”

Stabilization of LPV systems

“…As an example, a coarse application of the Lyapunov-based synthesis techniques available for linear systems is impossible, as it leads to solve an infinite number of linear matrix inequalities (LMIs). At this poinf two types of methods are usually used (see the recent works [8], [6] on LPV systems):…”