Time-triggered and event-triggered control of switched affine systems via a hybrid dynamical approach

Abstract

This paper focuses on the design of both periodic time-and event-triggered control laws of switched affine systems using a hybrid dynamical system approach. The novelties of this paper rely on the hybrid dynamical representation of this class of systems and on a free-matrix min-projection control, which relaxes the structure of the usual Lyapunov matrix-based min-projection control. This contribution also presents an extension of the usual periodic time-triggered implementation to the event-triggered one, where the control input updates are permitted only when a particular event is detected. Together with the definition of an appropriate optimization problem, a stabilization result is formulated to ensure the uniform global asymptotic stability of an attractor for both types of controllers, which is a neighborhood of the desired operating point. Finally, the proposed method is evaluated through a numerical example.

Event‐triggered output tracking control for switched systems: An adaptive stay interval scheme

“…Theorem 2. For ∀i, j ∈ N, i ≠ j, given positive scalars T k , 𝜀 i , 𝓁 m , 𝛽 m , 𝜏, 𝛾, and 𝜇 ≥ 1, if there are positive definite matrices P i , Q i , R i , M i , N i , ϝ i and matrices G i , H i satisfy ( 14) and (15), such that…”

“…Then, combine condition (A1), (37) can be received from (28). By using the Schur complement lemma to deal with (15), one has Multiply both sides of (A3) by diag{X j I}, one obtains…”

“…For example, the event‐triggered $$$ {H}_{\infty } $$$ safety control, 7,8 the robust fault tolerant control, 9 the observer‐based adaptive fuzzy funnel control, 10 the fault detection filtering, 11 and the finite‐time filtering 12 . Meanwhile, various types of switched systems have been studied, such as switched stochastic systems, 13,14 switched affine systems, 15 switched linear parameter‐varying systems, 16 switched Markov systems, 17,18 and switched positive systems 19 …”

“…Besides, the parameters 𝜆 1 = 1.98, 𝜆 2 = 2.84, 𝜆 3 = 0.72, 𝜆 4 = 1.64, 𝜆 5 = 1.0, 𝜆 6 = 10.22, 𝜆 7 = 0.5, 𝜆 8 = 0.25, 𝜆 9 = 0.25, 𝜆 10 = 0.1, and 𝜆 11 = 0.1 are chosen. The exogenous disturbance is 𝜔(t) = { 0.03 sin(2𝜋t), t ∈ [2, 15), 0, t ∈ [0, 1) ∪[15, 50). Then, conditions (37)-(39) are solved by LMIs, the corresponding tracking controller gains are obtained as…”

Control of Power Converters With Hybrid Affine Models and Pulse-Width Modulated Inputs

“…Inspired by [32], this section presents a controller for the hybrid system (8)-( 11) providing uniform global asymptotic stability (UGAS) of the compact set A.…”