Design of robust non-fragile H-infinity controllerbased on Delta operator theory

Considering that the controller parameters are of additive norm-bounded uncertainties when realized, a design method of robust non-fragile H-infinity controller for uncertain systems based on Delta operator theory is illustrated in this paper. A sufficient and necessary condition of the existence for the controller is given, which is presented in LMI forms. Finally, the designed method is used in the speed control system of a permanent magnet linear synchronous motor （PMLSM）. With the designed controller, the resulting speed closed-loop system is still stable and has the expected Hinfinity performance even if the sample period is reduced and the parameters of the controller and the controlled object are varied. The results show that the designed method is effective.

Nonfragile guaranteed cost control for Delta operator-formulated uncertain time-delay systems

With consideration that the controller parameters may vary from the designed value when the controller is realized, based on Lyapunov stability theory, a design method of nonfragile guaranteed cost control for a class of Delta operator-formulated uncertain time-delay systems is studied. A sufficient condition for the existence of the nonfragile guaranteed cost controller is given. A numeric example is then given to illustrate the effectiveness and the feasibility of the designed method. The results show that even if the parameters of the designed controller are of variations, the closed-loop system is still asymptotically stable and the super value of the cost function can also be obtained, while the closed-loop system will be unstable if the variations of the controller parameters are not considered when the controller is designed. The nonfragile guaranteed cost controller derived from the traditional shift operator method may cause the closed-loop system to be unstable, while the nonfragile guaranteed cost controller based on Delta operator method can avoid the unstable problem of the closed-loop system.

Observer-based H-infinity output feedback control with feedback gain and observer gain variations for Delta operator system

Considering that the controller feedback gain and the observer gain are of additive norm-bounded variations, a design method of observer-based H-infinity output feedback controller for uncertain Delta operator systems is proposed in this paper. A sufficient condition of such controllers is presented in linear matrix inequality （LMI） forms. A numerical example is then given to illustrate the effectiveness of this method, that is, the obtained controller guarantees the closed-loop system asymptotically stable and the expected H-infinity performance even if the controller feedback gain and the observer gain are varied.

Improved Parameter-dependent H_∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.

On a Pair of Operator Series Expansions Implying a Variety of Summation Formulas

With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.

State feedback design for singularly perturbed system using unified approach

The state feedback design for singularly perturbed systems described in Delta operator is considered. The composite state feedback controller for slow and fast subsystems is designed by using the direct method. The obtained results can bring previous conclusions of continuous and discrete time systems into the unified Delta framework. A simulation example is presented to demonstrate the validity and efficiency of the design.

Fault Detection for Uncertain Delta Operator Systems with Two-Channel Packet Dropouts via a Switched Systems Approach

This paper utilizes a switched systems approach to deal with the problem of fault detectio for uncertain delta operator networked control system with packet dropouts and timevarying delays.Uncertainties exist in the matrices of the systems and are norm-bounded time-varying.Two parts of packet dropouts are considered in this paper:From sensors to controllers,and from controllers to actuators.Two independent Bernoulli distributed white sequences are introduced to account for packet dropouts.Then an FD filter is designed under an arbitrary switching law.Furthermore,the sufficient conditions for the NCSs under consideration that are exponentially stable in the mean-square sense and satisfy H∞performance are obtained in terms of linear matrix inequalitie,multiple Lyapunov function and average dwell-tim approach.The explicit expression of the desired filter parameters is given.Finally,a numerical example verifies the effectiveness of the proposed method.

An Adaptive Sliding Mode Control of Delta Operator Systems with Input Nonlinearity Containing Unknown Slope Parameters

The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality(LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.

A unified direct approach for discretizing fractional-order differentiator in delta-domain

Fractional-order differentiator is a principal component of the fractional-order controller.Discretization of fractional-order differentiator is essential to implement the fractionalorder controller digitally.Discretization methods generally include indirect approach and direct approach to find the discrete-time approximation of fractional-order differentiator in the Z-domain as evident from the existing literature.In this paper,a direct approach is proposed for discretization of fractional-order differentiator in delta-domain instead of the conventional Z-domain as the delta operator unifies both analog system and digital system together at a high sampling frequency.The discretization of fractional-order differentiator is accomplished in two stages.In the first stage,the generating function is framed by reformulating delta operator using trapezoidal rule or Tustin approximation and in the next stage,the fractional-order differentiator has been approximated by expanding the generating function using continued fraction expansion method.The proposed method has been compared with two well-known direct discretization methods taken from the existing literature.Two examples are presented in this context to show the efficacy of the proposed discretization method using simulation results obtained from MATLAB.