Stabilization for discrete-time LPV systems with Markovian switching under partially known transition probabilities

This paper investigates the guaranteed cost control problem for a class of linear parameter-varying (LPV) systems with Markovian switching under partly known transition rates. A key point of this work relaxes Markovian jump systems whose subsystems are described by linear time-invariant (LTI) dynamics to LPV systems with Markovian switching whose subsystems are described by LPV dynamics. Meanwhile, the special assumption of completely known transition rates is relaxed to more general case that transition rates are partly known. Moreover, the proposed control technique for the LPV systems with Markovian switching is used to solve the guaranteed cost control problem of turbofan-engine. Firstly, a guaranteed cost controller is designed, and the design problem can be reduced to a set of linear matrix inequalities (LMIs) feasibility problem. Then, a turbofan-engine example is given to demonstrate the applicability of the main results.

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Frequency Response Functions of Linear Parameter-Varying Systems

Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions

This work is devoted to interval observers design for discrete-time Linear Parameter-Varying (LPV) systems under assumption that the vector of scheduling parameters is not available for measurements. Two scenarios are considered: a pure estimation and an output stabilizing feedback design. Stability conditions are expressed in terms of linear matrix inequalities. The efficiency of the proposed approach is demonstrated through computer simulations.

In this paper, we consider the fault Detection and isolation (FDI) problem for faulty linear parameter-varying (LPV) systems subject to disturbances and propose a observer-based solution by using multiobjective optimization techniques. To simply the design process, a general faulty LPV system will be constructed from standard LPV description by converting actuator/system component faults into sensor faults at first. Then a bank of LPV FDI filters will be designed to identify each fault. Each FDI filter could generate a residual signal to track individual fault with minimum error and suppressing the effects of disturbances and other fault signals. The design of FDI filters will be formulated as multiobjective optimization problems in terms of linear matrix inequalities (LMIs) and can be solved efficiently. Two numerical examples are also presented to demonstrate the proposed fault detection and isolation approach on both LPV and LTI systems.

Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers

This paper proposes a comprehensive mixed-sensitivity control design for an experimental magnetic levitation (Maglev) system. The control strategy can be seen as an extension of the loop-shaping procedure for discrete-time linear parameter-varying (LPV) systems using linear-fractional representation (LFR). By making use of an efficient quadratic approach given in the form of linear matrix inequalities (LMIs), a functional and computationally attractive gain-scheduling technique is achieved. Despite the rigorous mathematical considerations to obtain the controller, the guidelines to its practical implementation are presented as a straightforward method using LMIs. A detailed modeling of the Maglev plant manufactured by Quanser is carried out to illustrate the procedure, including a description of the nonlinear equations embedding process to obtain a discretized quasi-LPV (qLPV) model. Experimental results demonstrate the effectiveness of the proposed control design.

This paper presents a new dilated linear matrix inequality (LMI) representation to design a state feedback controller and a dynamic feedforward disturbance compensator for linear parameter-varying (LPV) systems. The improved LMIs are convex and finite-dimensional without any iterative approach. The designs are based on a new proposed equivalent bounded real lemma (BRL) by means of matrix dilation for LPV systems and uncertain linear systems under time-varying parametric uncertainties (TVPUs). This dilated BRL provides lower conservative results than existing methods in terms of robust stability. Accordingly, a dynamic disturbance compensator is designed in addition to a state feedback controller. This paper mainly focuses on the design of compensators against disturbances in addition to the design of state feedback controllers. The dynamic matrices of the compensator change with the time-varying parameters of the LPV or uncertain system during operation, assuming that the disturbances and the parameters are measurable or observable. The compensator can be designed to attenuate the disturbances/noises or to improve reference tracking. Finally, numerical and simulation outcomes are presented to prove both the effectiveness and lower conservativeness of the proposed LMIs.

Linear Parameter Varying (LPV) system shows preferable performance in dealing with NonLinear (NL) systems and systems with time-varying parameters, based on a kind of wheel-legged robot with two-wheel and balance as Inverted Pendulum, this paper proposes a gain scheduling control method for balancing using LPV system on Equivalent model with Center Of Mass (COM). In order to ensure the stability and responsive of the system with possible values for all variable parameters, Higher Order Singular Value Decomposition (HOSVD) is used for constructing polytopic LPV system, then the robust controller is designed for the vertex systems forthputting Linear Matrix Inequality (LMI) approach, and the gain scheduling controller for global system is obtained by convex combination of vertex LTI systems. The simulation results show that the system can achieve the expected indicators.

This technical article presents novel robust stabilization conditions for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). The proposed conditions rely on the use of slack variables and decision matrices associated with the LFR approach to provide new controller designs. In addition, we address parameter-dependent Lyapunov functions and full-block multipliers to obtain less conservative synthesis conditions for discrete-time LPV/LFR systems. Design conditions are cast in the form of linear matrix inequalities to generate robust state-feedback and output-feedback controllers. Numerical examples demonstrate the effectiveness of the proposed method.

We introduce a controller design methodology for nonlinear systems via complementary Linear Parameter Varying (LPV) controller and observer structures. The recently developed method is able to control physiological systems even with complex nonlinearities — without using Linear Matrix Inequalities (LMI) or other techniques requiring iterations. The developed method is based on the classical state feedback theorems, matrix similarity theorems and supplementary controller and observer structure which efficiently uses the mathematical properties of the parameter space of the LPV system. The main benefits of the proposed method is that the controller design does not require mathematical tools needing iteration thus high computational capacity. We used a nonlinear compartmental model in order to demonstrate the application of the method. The results showed that the developed complementary LPV controller and observer structures perform well on both the LPV systems and the original nonlinear system as well.

This paper proposes a control oriented identification framework for a class of linear parameter-varying (LPV) systems, that takes into account both the dependence of part of the model on time-varying parameters as well as the possible existence of a nonparametric component. The main result of the paper shows that the problems of establishing consistency of the data and of obtaining a nominal model for these systems can be recast as a linear matrix inequality feasibility problem that can be efficiently solved. These results are illustrated with a practical example arising in the context of active vision.

This paper presents a controller design method for dealing with the induced ℒ 2 -norm problem for switched linear parameter-varying (LPV) systems. Considering the arbitrary switchings caused by the parameters varying, a common parameter-dependent Lyapunov function is employed to derive sufficient linear matrix inequality (LMI) conditions for the switched LPV systems. A family of LPV controllers are designed according to the LMI conditions, and each of them is suitable for the corresponding parameter region. The proposed switching LPV control method is applied to an F-16 aircraft longitudinal model and simulation results demonstrate the effectiveness of the approach.

This paper addresses the design problem of Gain-Scheduled Output-Feedback (GSOF) controllers for discretetime Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). In our problem setting, it is supposed that scheduling parameters are provided with some uncertainties. In this practical problem setting, we give a sufficient condition for designing GSOF controllers exploiting the uncertain scheduling parameters which minimize the induced l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm in terms of Parameter-Dependent Bilinear Matrix Inequalities (PDBMIs). Two algorithms for solving the PDBMIs, i.e. line search and iterative algorithms, are shown. Under the ideal situation, i.e. exact values of scheduling parameters are available, our method then recovers the conventional design method via PDLFs.