An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

Robustness analysis of linear time-varying systems with application to aerospace systems

In recent years significant effort was put into developing analytical worst-case analysis tools to supplement the Verification \& Validation (V\&V) process of complex industrial applications under perturbation. Progress has been made for parameter varying systems via a systematic extension of the bounded real lemma (BRL) for nominal linear parameter varying (LPV) systems to IQCs. However, finite horizon linear time-varying (LTV) systems gathered little attention. This is surprising given the number of nonlinear engineering problems whose linearized dynamics are time-varying along predefined finite trajectories. This applies to everything from space launchers to paper processing machines, whose inertia changes rapidly as the material is unwound. Fast and reliable analytical tools should greatly benefit the V\&V processes for these applications, which currently rely heavily on computationally expensive simulation-based analysis methods of full nonlinear models. The approach taken in this thesis is to compute the worst-case gain of the interconnection of a finite time horizon LTV system and perturbations. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQC). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory. This utilizes a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can then be efficiently solved using custom-tailored meta-heuristic (MH) algorithms. One of the developed algorithms is initially benchmarked against non-tailored algorithms, demonstrating its improved performance. A second algorithm's potential application in large industrial problems is shown using the example of a touchdown constraints analysis for an autolanded aircraft as was as an aerodynamic loads analysis for space launcher under perturbation and atmospheric disturbance. By comparing the worst-case LTV analysis results with the results of corresponding nonlinear Monte Carlo simulations, the feasibility of the approach to provide necessary upper bounds is demonstrated. This comparison also highlights the improved computational speed of the proposed LTV approach compared to simulation-based nonlinear analyses

Robustness analysis of linear time-varying systems with application to aerospace systems

In recent years significant effort was put into developing analytical worst-case analysis tools to supplement the Verification \& Validation (V\&V) process of complex industrial applications under perturbation. Progress has been made for parameter varying systems via a systematic extension of the bounded real lemma (BRL) for nominal linear parameter varying (LPV) systems to IQCs. However, finite horizon linear time-varying (LTV) systems gathered little attention. This is surprising given the number of nonlinear engineering problems whose linearized dynamics are time-varying along predefined finite trajectories. This applies to everything from space launchers to paper processing machines, whose inertia changes rapidly as the material is unwound. Fast and reliable analytical tools should greatly benefit the V\&V processes for these applications, which currently rely heavily on computationally expensive simulation-based analysis methods of full nonlinear models. The approach taken in this thesis is to compute the worst-case gain of the interconnection of a finite time horizon LTV system and perturbations. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQC). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory. This utilizes a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can then be efficiently solved using custom-tailored meta-heuristic (MH) algorithms. One of the developed algorithms is initially benchmarked against non-tailored algorithms, demonstrating its improved performance. A second algorithm's potential application in large industrial problems is shown using the example of a touchdown constraints analysis for an autolanded aircraft as was as an aerodynamic loads analysis for space launcher under perturbation and atmospheric disturbance. By comparing the worst-case LTV analysis results with the results of corresponding nonlinear Monte Carlo simulations, the feasibility of the approach to provide necessary upper bounds is demonstrated. This comparison also highlights the improved computational speed of the proposed LTV approach compared to simulation-based nonlinear analyses

Feasibility studies of promising stability and gravity /including zero-G/ experiments for manned orbiting missions Final report, 17 Dec. 1964 - 17 Dec. 1965

Feasibility of stability and gravity experiments for manned orbiting mission

Design of tracking systems incorporating multivariable plants

The methodology for the design of error-actuated digitalset-point tracking controllers proposed by Porter andco-workers has emerged as a result of the pursuit of effective and practical solutions to the problem of designing digital control systems for unknown, dynamically complex multivariable plants with measurable outputs. In this thesis, such digital set-point tracking controllers and the resulting digital set-point tracking systems are enriched to embrace plants with unmeasurable outputs and plants with more outputs than manipulated inputs. In the study of the latter plants, the novel concepts of limit tracking (i.e. the tracking exhibited by plants with moreoutputs than inputs) is introduced and an associatedmethodology for the design of self-selecting controllers isproposed. Such controllers involve the selection of differentset-point tracking controllers to control the most criticalsubset of plant outputs based upon the developed rigoroustheoretical foundations for the limit-tracking systems. Insuch foundations, the classification of linear multivariableplants into Class I and Class II plants based upon theirsteady-state transfer function matrices facilitates theassessment of the feasibility of limit-tracking systems.Furthermore, the associated order-reduction techniquesimplifies the problem of deciding the minimum numbers ofdifferent subsets of plant outputs to be controlled bycorresponding set-point tracking controllers. In addition, the dynamical properties of limit-tracking systems are alsoinvestigated using the phase-plane method and a methodology for the design of supervisory self-selecting controllers is proposed so as to prevent the occurrence of dynamical peculiarities such as limit-cycle oscillations which might happen in limit-tracking systems. The effectiveness of all the proposed methodologies and techniques is illustrated by examples, and the robustness properties of set-point tracking systems and limit-tracking systems in the face of plant variations and unknown disturbances are tested. Finally, self-selecting controllers are designed for a nonlinear gas-turbine engine and their practical effectiveness is clearly demonstrated

Aeronautical engineering: A special bibliography with indexes, supplement 41, February 1974

This special bibliography lists 514 reports, articles, and other documents introduced into the NASA scientific and technical information system in January 1974