Stability Criteria for Time-Delay Systems From an Insightful Perspective on the Characteristic Equation

H∞ Robust Fault-Tolerant Control of a Six-Rotor UAV Containing Sensor Faults and Actuator Non-Affine Faults

“…Theorem 3. With positive parameters δ, γ, κ, η, λ 1 , λ 2 , λ 3 , the system ( 14) is stable and has H ∞ performance index γ when there exist matrices W 11 dt , W 22 dt > 0, K dt such that the following two inequalities hold,…”

“…For systems with variable time lags where the state is not fully measurable [9], a sliding surface can be constructed in the error space and observation space of the system separately so that the system can reach the steady state in a relatively short time after estimating the system state. Stefano et al combined the variable time lags of the system and designed a controller so that the system can converge in a finite time under the constraints [10].Tessina H. Scholl and Lutz Gröll proposed a new stability criterion for discrete time lag continuous systems independent of time lag [11]. To achieve fast stabilization of a class of variable time lag systems, [12] used Lyapunov-Krasovskii function (LKF) to obtain sufficient conditions for system stability, which finally ensured global stability of the system and obtained good control results.…”

Estimating the delay margin for stability of linear delay systems by the weighted matrix measure

“…Notably, some of these approaches can compute the exact delay margin without any additional conservatism. 18,19,22 Most of the mentioned works for the delay margin problems are concerned with single-delay systems. To our knowledge, studies on delay margin problem of linear systems with multiple incommensurate delays are scarce.…”

“…By means of frequency sweeping tools and factorization of the corresponding characteristic function of system, Reference 21 presents a scalable approach to compute the delay margin of a class of neutral‐type delay systems. Based on the spectral abscissa, Reference 22 formulates a constrained minimization problem that gives the delay interval of stability for delay systems. In addition, delay margin problems for low‐order systems with PID controllers are discussed in References 23 and 24.…”

“…The frequency‐domain approaches are effective in dealing with single delay cases. Notably, some of these approaches can compute the exact delay margin without any additional conservatism 18,19,22 …”