Nonlinear H∞ feedback control with integrator for polynomial discrete-time systems

Saat, Shakir; Nguang, Sing Kiong; Darsono, A. M.; Azman, Noorazma

doi:10.1016/j.jfranklin.2014.04.019

Cited by 20 publications

(21 citation statements)

References 55 publications

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“…then we get: (31) For the simplification of entropy measurement for the LPDS in Equation (1) Based on the finite difference approximation in Equation (28), the LPDS in Equation (1) can be represented by the following finite difference system:…”

Section: The System Entropy Measurement Of Lspdss Via a Semi-discretimentioning

confidence: 99%

“…Hence, in this study, we will measure the system entropy of SPDSs from the system's characteristics. Actually, many real physical and biological systems are only nonlinear, such as the large-scale systems [25][26][27][28], the multiple time-delay interconnected systems [29], the tunnel diode circuit systems [30,31], and the single-link rigid robot systems [32]. Therefore, we will also discuss the system entropy of nonlinear system as a special case in this paper.…”

Section: Introductionmentioning

confidence: 99%

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System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

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System entropy describes the dispersal of a system's energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs) in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton-Jacobi integral inequality (HJII)-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs). To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3). Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

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Section: The System Entropy Measurement Of Lspdss Via a Semi-discretimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

System Entropy Measurement of Stochastic Partial Differential Systems

Chen

Hsieh

2016

Entropy

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“…Moreover, the controller design problems for systems with both actuator and sensor saturations have been developed in [14,27,15,31,45]. To avoid the nested saturations, most of the references adopt dynamic output-feedback control strategy [8,26].…”

Section: Introductionmentioning

confidence: 99%

Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

Wen

Nguang

2016

Information Sciences

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“…Nonlinear static output feedback results have been derived for fuzzy systems: [13], [14] addresses static output feedback controllers for Takagi-Sugeno fuzzy models with linear and linear time-delay subsystems; for polynomial fuzzy systems a sum-of-squares approach is used in [15]. In [16] a static output feedback method with integral action is proposed for discrete-time polynomial systems. Other research directions on nonlinear static output feedback include sampled-data control systems consisting of a nonlinear plant in feedback with an output-feedback sampled-data polynomial controller [17].…”

Section: Introductionmentioning

confidence: 99%

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Baldi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-ofSquares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

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Nonlinear H∞ feedback control with integrator for polynomial discrete-time systems

Cited by 20 publications

References 55 publications

System Entropy Measurement of Stochastic Partial Differential Systems

System Entropy Measurement of Stochastic Partial Differential Systems

Stochastic finite-time boundedness on switching dynamics Markovian jump linear systems with saturated and stochastic nonlinearities

An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

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