Insensitive output feedback H_∞ control of delta operator systems with insensitivity to sampling time jitter

Abstract

SUMMARYThe insensitive multi-objective H 1 control synthesis problem via dynamic output feedback for linear delta operator systems with insensitivity to sampling time jitter is investigated in the case of small sampling times. The delta-domain model instead of the standard shift-domain model is used to avoid the inherent numerical ill-condition resulting from using the latter model at high sampling rates. Parameter sensitivity function of the transfer function with respect to sampling time is defined to mitigate the effect of sampling time jitter because it may cause significant degradation of the overall system performance. It is worth pointing out that a novel bounded real lemma for delta operator allowing extra degree of freedom for multi-objective control design is presented by using the well-known projection lemma. Then, from this new lemma, a twostep design procedure based on LMI is presented to design insensitive dynamic output feedback controllers such that the resulting closed-loop system is asymptotically stable and meets the requirement of sensitivity specification. A numerical example is also presented to show the effectiveness of the proposed method.

H∞ Preview Control of A Class of Uncertain Discrete‐Time Systems

“…Actually, based on Lemma 6 in , the robust H ∞ control problems were considered by . Therefore, the obtained results may generalize the relevant results in .…”

“…In fact, by setting T 1 = 0, T 2 = − P , this condition of Theorem is transformed into Lemma 6 in . Actually, based on Lemma 6 in , the robust H ∞ control problems were considered by . Therefore, the obtained results may generalize the relevant results in .…”

“…Actually, based on Lemma 6 in [30], the robust H ∞ control problems were considered by references [31][32][33]. Therefore, the obtained results may generalize the relevant results in [31][32][33]. Now, the purpose of the preview control is to design a state feedback controller for system (25) in the form of…”

Sliding mode fault‐tolerant control of uncertain system: A delta operator approach

“…Therefore, it is useful and valuable to apply delta operator in system modeling and analysis. Recently, based on the delta operator approach, many stability and stabilization results for control systems have been reported . The work in designed a robust sliding mode controller for uncertainty time delay systems via the delta operator approach.…”

“…u F is the faulty control input satisfying(4) andIn this simulation procedure, we aim to validate (i) the estimation effect for the bounds of the unknown actuator efficiency factor à and the unknown bounded time-varying fault deviation Á.t k / and (ii) the stabilization electiveness for the simulated truck-trailer plant under exogenous disturbance environment when applying the designed adaptive SMC law(18).Assume a fault deviation Á.t k / D 0:06 0:03 sin.t k / and an external disturbance w.t k / D 0:04 0:02rand.t k /, where rand(t k ) denotes that a real number is randomly generated in the interval (0,1) at time instance t k . Then the parameters˛D 0,ˇD l D 2:8, Á D 0:03, Á D 0:09, w D 0:02, and w D 0:06.…”