Reachability and stabilization of scheduled steady-states for LPV single-input systems

Abstract

The aim of this work is characterizing the class of LPV systems that admit steady-state trajectories depending exclusively on the scheduling parameter. In particular, it will be shown that only certain parameter dependent steady-state profiles are admissible and can be reached by means of a suitable control input. Furthermore, the asymptotic stability and the stabilization of such steady-states is investigated using Lyapunov-based techniques. Extensive numerical simulations illustrate and corroborate the theoretical results.

Designing controller parameters of an LPV system via design space exploration

“…In (1), 𝛼𝛼 ∈ ℝ 𝑑𝑑 is a vector of some unknown and time-invariant design parameters that should be precisely adjusted to establish LPV system's stability. It is assumed that 𝛼𝛼 belongs to a given convex polygonal space 𝜙𝜙 ⊂ ℝ 𝑑𝑑 that is denoted by the design space.…”

“…Obviously, for the stability analysis of this system, we need to show the system (1) is stable for time-varying 𝜌𝜌(𝑡𝑡). This paper utilizes the concept of instability since the instability analysis of system (1) can be shown even if the system is unstable for a specific constant 𝜌𝜌̅ .…”

“…The linear parameter varying (LPV) framework is widely applicable for equivalently or approximately modeling of time-varying or nonlinear dynamic behaviors of control systems [1]. Various methods are employed to convert control systems into LPV systems [1].…”

“…The linear parameter varying (LPV) framework is widely applicable for equivalently or approximately modeling of time-varying or nonlinear dynamic behaviors of control systems [1]. Various methods are employed to convert control systems into LPV systems [1]. Among these methods, performing exact mathematical transformations to model nonlinear dynamics in varying parameters [2], approximating the Jacobian linearization of nonlinear systems around some equilibrium interest points [3], and exploiting data-driven identification [4] have gained the utmost importance.…”