H2 gain scheduled state feedback for LPV system with new LMI formulation

The paper presents stabilization of a Networked Control System (NCS) with uncertain, time-varying delays using two stabilization approaches namely, Parameter Dependant Lyapunov Function (PDLF) and Quadratic Lyapunov Function (QLF). The PDLF approach depends upon the time varying delay parameters. Thus, for larger delays the system's stability is ensured. In NCS, the uncertainties arising out from the variations in time-delay is modeled using polytopic approach and the stability region of the system is presented in terms of controller gain and maximum tolerable delay. The overall NCS is represented in discrete domain. The proposed PDLF stabilization results have been compared with that of the QLF approach. Lyapunov-based stability criterion is presented in Linear Matrix inequalities (LMIs). The stabilized state feedback controller is designed using LMIs and considering the bounded time-varying delays. The proposed approach is illustrated by two numerical examples. From the results obtained, it is observed that the PDLF approach improves the stability region of the system.

This article addresses the admissibility analysis and state-feedback control synthesis problems of discrete-time polytopic descriptor systems with possibly time-varying parameters. First, we present a new necessary and sufficient strict linear matrix inequality (LMI) condition for the admissibility analysis of linear time-invariant (LTI) descriptor systems. Then, based on the concept of poly-quadratic admissibility, introduced in this article, we extend this result to the admissibility analysis of possibly time-varying parameter-dependent descriptor systems. This extension, which applies to both uncertain and measurable parameters, uses parameter-dependent Lyapunov functions and employs two slack variables. The extended conditions are also expressed as strict LMI conditions which are easily tractable numerically compared to the non-strict ones often encountered when dealing with descriptor systems. Note that we have proposed two separate admissibility analysis conditions: one directly exploitable for state estimation and the other for state-feedback control. The need for different admissibility analysis conditions for each synthesis problem is motivated by the fact that the duality between state estimation and state-feedback control, which hold in the case of measurable parameters, does not hold when dealing with uncertain ones. In our approach, we overcome the absence of such duality by considering a dilation only on the dynamical part of the descriptor system. The application of our analysis result to both robust state-feedback control and polytopic state-feedback control are also presented in this article. Our analysis results extend to descriptor systems, some existing results developed for regular systems.

The article proposes a novel approach to robust stability analysis of linear parameter-varying systems, of which the system matrix is polynomial-dependent on a time-varying parameter with degree L. The robust asymptotically stability of the system is transformed into feasibility test of a pair of linear matrix inequalities (LMIs) that include the parameter, its varying-rate bound and given coefficient matrices. The result presented in this article is less conservative comparing with the previous results that are based on either quadratic Lyapunov function, or a parameter-dependent Lyapunov function, respectively. A numerical example shows the validity of the result.

This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-/spl mu/ analysis, and numerical experiments indicate that they often compare favorably with /spl mu/ analysis for time-invariant parameter uncertainty.

Discrete-Time LPV Controller Synthesis Using Dilated LMIs with Application to an Arm-Driven Inverted Pendulum

The problem of robust constrained model predictive control (MFC) of systems with polytopic uncertainty is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.

This paper presents a novel H/spl infin/ formulation to design a reliable tracking controller for a discrete LTI aircraft system against actuator outage faults and control surface impairment modelled as polytopic uncertainties. Both the style-feedback and output-feedback cases are considered. The approach is based on multiobjective optimization using several parameter dependent Lyapunov functions, each corresponding to a vertex of the uncertainty polytope. The main advantage of this approach with respect to the other well-known techniques is the reduced conservativeness. In the output-feedback case, a new linear matrix inequality (LMI) formulation is derived and solved by an iterative LMI (ILMI) algorithm. Finally, the application to a nonlinear F-16 aircraft model with actuator outage faults and control surface impairment illustrates the effectiveness of the proposed approach.

In this paper, the problem of designing Robust Gain-Scheduling observers for continuous-time Linear Parameter-Varying systems via parameter-dependent Lyapunov function is addressed. The scheduling parameters are assumed to be imprecisely measured, i.e., corrupted with additive noise. Multi-simplex modeling approach is utilized to model the time-varying parameters and associated uncertainties. Sufficient conditions are given for the synthesis problem in terms of Parameterized Linear Matrix Inequalities. The designed observer not only guarantees asymptotic stability of estimation error dynamics but also minimizes the estimation errors under exogenous disturbances. Both, ℋ 2 and ℋ ∞ performances have been considered. An illustrative numerical example is presented to demonstrate the benefit of the developed approach.

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

The paper applies several concepts in robust control research such as linear matrix inequalities, edge theorem, parameter-dependent Lyapunov function, and Popov criteria to investigate the stability property of Hopfield-type neural networks. The existence and uniqueness of an equilibrium is formulated as a matrix determinant problem. An induction scheme is used to find the equilibrium. To verify whether the determinant is nozero for a class of matrix, a numerical range test is proposed. Several robust control techniques in particular linear matrix inequalities are used to characterize the local stability of the neural networks around the equilibrium. The global stability of the Hopfield neural networks is then addressed using a parameter-dependent Lyapunov function technique. All these results are shown to generalize existing results in verifying the existence/uniqueness of the equilibrium and local/global stability of Hopfield-type neural networks.

This paper deals with the stabilization and the H 2 control synthesis of Linear Parameter Varying (LPV) descriptor systems. The compensator design problem is examined through a parameter-dependent observer-based control structure. The proposed approach uses parameter-dependent Lyapunov functions and involves slack variables in order to achieve less restrictive synthesis conditions. These synthesis conditions are expressed as a Linear Matrix Inequality (LMI) solvability problem. The admissibility and the H 2 performance are ensured by computing appropriate gains of the state-feedback controller and the observer. Simulation results obtained with a numerical example, show the effectiveness of the proposed approach.

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In this paper, the output feedback controller is designed for the 2D discrete (T-S) fuzzy systems expressed by Fornasini-Marchesini II Model. Our aim is to develop static output feedback controller (SOF) so that the addressed closed loop system globally asymptotically stable. By using the fuzzy-basis-dependent Lyapunov function only, sufficient conditions are given in form of linear matrix inequalities (LMIs) to guarantee the 2D closed loop system to be globally asymptotically stable. The main advantage is design a SOF controller is that no constraints are imposed on system matrices. Illustrative example is given to show the potential and usefulness of the proposed results.

We propose a less conservative linear matrix inequalities (LMIs) condition for ℋ∞ performance analysis and synthesis of discrete-time linear parameter varying (LPV) systems. The time varying parameter is represented by a linear fractional form. Sufficient conditions for ℋ∞ performance and controller synthesis are given in terms of a finite number of LMIs using parameter dependent Lyapunov functions.

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. First, the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we give stabilization conditions for closed-loop fuzzy systems with parametric uncertainties. Second, all the conditions are formulated in the format of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. A numerical example of the chaotic Lorenz system is given to illustrate the utility of the fuzzy Lyapunov function approach.