Control design for linear systems with saturating actuators and ℒ/sub 2/-bounded disturbances

SUMMARYIn this paper, we study the problem of disturbance attenuation by output feedback for linear systems subject to actuator saturation. A nonlinear output feedback, expressed in the form of a quasi-linear parametervarying system with state-dependent scheduling parameter, is constructed that leads to the attenuation of the effect of the disturbance on the output of the system. The level of disturbance attenuation is measured in terms of the restricted L 2 gain and the restricted L 2 -L ∞ gain over a class of bounded disturbances.

Section: Theoremmentioning

confidence: 99%

Disturbance attenuation by output feedback for linear systems subject to actuator saturation

Zheng

Lin

2008

“…In particular, for unstable open-loop systems, the possibility of having both non-null initial conditions and potentially destabilizing disturbances cannot be neglected. In this case only local finite gain L 2 -stabilization can be ensured [6][7][8].…”

Section: Introduction Consider the Following Continuous-time Systemmentioning

confidence: 97%

“…A modified sector condition, recently proposed in [9]: this condition encompasses the classical one applied for instance in [7,8] to represent the actuator saturation, and, furthermore, it allows to formulate conditions in the LMI form and to reduce the conservatism of the results. 2.…”

Section: Introduction Consider the Following Continuous-time Systemmentioning

confidence: 99%

“…On the other hand, relation (8) implies that the set S 1 ¼ EðP; 1=mÞ SðK À E; rÞ with 1=m ¼ b þ 1=Zd: Furthermore, note that from the definition of m; one gets S 0 ¼ EðP; bÞ EðP; 1=mÞ:…”

mentioning

confidence: 98%

“…Thus, the proposed approach is adapted to treat multiple objective control problems in a potentially less conservative manner than LMI methods that associate a single Lyapunov function with the different control objectives. For instance, the following additional LMI condition can be considered if some temporal performance is required around the origin [8]:…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Castelan

Tarbouriech

Silva

et al. 2006

Self Cite

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.

Delay‐dependent anti‐windup strategy for linear systems with saturating inputs and delayed outputs

Tarbouriech

Silva

García

2004

Self Cite

SUMMARYThis paper addresses the problem of the determination of stability regions for linear systems with delayed outputs and subject to input saturation, through anti-windup strategies. A method for synthesizing antiwindup gains aiming at maximizing a region of admissible states, for which the closed-loop asymptotic stability and the given controlled output constraints are respected, is proposed. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear time-delay system with a dead-zone nonlinearity, constructive delay-dependent stability conditions are formulated by using both quadratic and Lure Lyapunov-Krasovskii functionals. Numerical procedures based on the solution of some convex optimization problems with LMI constraints are proposed for computing the anti-windup gain that leads to the maximization of an associated stability region. The effectiveness of the proposed technique is illustrated by some numerical examples.