ℒ︁₂‐Stabilization of continuous‐time linear systems with saturating actuators

Abstract

SUMMARYThis paper addresses the problem of controlling a linear system subject to actuator saturations and to L 2 -bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed-loop input-to-state stability (ISS) and the closed-loop finite gain L 2 stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition, which encompasses the classical sector-nonlinearity condition considered in some previous works, and Finsler's Lemma, which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework.

Stability Analysis and Stabilization of Systems With Input Backlash

“…As a second example, we consider an unstable F-8 aircraft MIMO example borrowed from [4], given by: To evaluate the degree of conservatism of the sets S0(Pan) and S0(Psynan) in which the trajectories are uniformly ultimately bounded, the time-evolution of x ′ Panx (solid line, associated to the control gain Kan) and x ′ Psynanx (dashed line, associated to the control gain Ksyn) are plotted in Figure 6. They show that, once the trajectory enters the ellipsoidal set S0(P ), i.e.…”

Entwurf von modellbasierten Anti-Windup-Methoden für Systeme mit Stellbegrenzungen

“…Semiglobale Ergebnisse wurden in [125,127,163] publiziert. Lokale Stabilität des Ursprungs garantieren die Reglerentwürfe [31,74,91,93]. Durch eine Modifikation des Regelgesetzes können auch andere Ruhelagen stabilisiert werden [19,104,106].…”

“…Der in [31] vorgestellte Zustandsreglerentwurf gibt hinreichende Bedingungen für die Matrix K in Form linearer Matrixungleichungen an, die obige Anforderungen sicherstellen. Die Grundidee ist, das Gebiet G u durch eine Höhenlinie der quadratischen Ljapunov-Funktion …”

“…dass die Realteile der Eigenwerte von A s − B s,u K kleiner als −λ sind [31]. Der Zustandsreglerentwurf lässt sich folglich als konvexes Optimierungsproblem formulieren.…”

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

“…The analysis and synthesis problems for the deterministic linear systems with actuator saturation have been widely studied (see, e.g., [7][8][9][10][11][12][13][14][15][16], and the references therein). Hu et al [14,15] presented a new method to deal with the saturation nonlinearity, i.e., placing the saturation function into a convex hull.…”