Linear Delta Operator Systems Research Articles

Stability analysis and design of cooperative control for linear delta operator system

<abstract><p>This paper investigates the cooperative state feedback control problem for delta operator-based large-scale systems with independent subsystems. First, the state feedback controller is introduced to interconnect the adjacent subsystems into a closed-loop system. Second, the Lyapunov function in delta domain is constructed, and the linear matrix inequality method is used to design the cooperative state feedback stability controller for the whole large-scale interconnected system. Third, a performance index is introduced for the design of the optimal cooperative state feedback controller. Finally, stability of the closed-loop system is proved on the basis of stability theory, and simulation examples are given for showing the effectiveness of the design method.</p></abstract>

Parametric delta operator Riccati equation and applications to semi-global stabilization in the presence of actuator saturation

In this paper, a parametric delta operator Riccati equation is established for low gain feedbacks of linear delta operator systems. Some properties for the parametric delta operator Riccati equation are given based on a parameter-dependent cost function. An explicit solution is also given for the delta operator parametric Riccati equation. Semi-global stabilization is described for a linear delta operator system with actuator saturation via low gain state and output feedback control laws. A numerical example is given to illustrate the effectiveness and potential for the developed techniques.

Output regulation for linear delta operator systems subject to actuator saturation

Summary In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti-stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd.

Stability analysis for delta operator systems subject to state saturation

ABSTRACTIn this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.

Robust control for Markovian jump delta operator systems with actuator saturation

In this paper, robust stochastic stabilization problems for uncertain Markovian jump linear delta operator systems with actuator saturation are considered. The definition of the domain of attraction for a Markovian jump delta operator system in mean square sense is introduced to analyze the stochastic stability of the closed-loop system. By using a stochastic Lyapunov function which is dependent on the jump mode, design procedures for a mode-dependent state feedback controller are developed based on linear matrix inequality approach. A mode-independent state feedback controller is also designed by using a mode-independent Lyapunov function. Some simulation results are given to illustrate the effectiveness of the developed techniques.

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

SUMMARYThe insensitive multi‐objective H ∞ 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 two‐step 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. Copyright © 2012 John Wiley & Sons, Ltd.

Low-sensitivity H ∞ filter design for linear delta operator systems with sampling time jitter

This article is concerned with the problem of designing H ∞ filters for a class of linear discrete-time systems with low-sensitivity to sampling time jitter via delta operator approach. Delta-domain model is used to avoid the inherent numerical ill-condition resulting from the use of the standard shift-domain model at high sampling rates. Based on projection lemma in combination with the descriptor system approach often used to solve problems related to delay, a novel bounded real lemma with three slack variables for delta operator systems is presented. A sensitivity approach based on this novel lemma is proposed to mitigate the effects of sampling time jitter on system performance. Then, the problem of designing a low-sensitivity filter can be reduced to a convex optimisation problem. An important consideration in the design of correlation filters is the optimal trade-off between the standard H ∞ criterion and the sensitivity of the transfer function with respect to sampling time jitter. Finally, a numerical example demonstrating the validity of the proposed design method is given.