Stability and stabilization for LPV systems based on Lyapunov functions with non-monotonic terms

Peixoto, Márcia L. C.; Pessim, Paulo S.P.; Lacerda, Márcio J.; Palhares, Reinaldo M.

doi:10.1016/j.jfranklin.2020.04.019

Cited by 32 publications

(14 citation statements)

References 32 publications

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“…F I G U R E 1 Domain of attraction estimation for the exact discrete-time system and state trajectories of the sampled-data system (27) in feedback with (8) designed with Lemma 3. Each trajectory is generated for a different value of -Example 1…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…As illustrated in Figure 3, as increases, the performance index log det (Q) related to the volume of the guaranteed domain of attraction estimation decreases, which indicates a commitment between sampling time and guaranteed performance. F I G U R E 2 Domain of attraction estimation for the exact discrete-time model and state trajectories of the sampled-data system (27) in feedback with (8) designed with Lemma 3. Each trajectory is generated for a different value of .…”

Section: Examplementioning

confidence: 99%

“…24 In this case, by following the sector nonlinearity approach, 24,25 nonlinear systems are generally rewritten as equivalent local polytopic differential inclusions by subsuming their bounded nonlinear expressions into parameters that compose the polytopic model and are also employed to construct the gain-scheduling control law. Then, mimicking developments for linear parameter-varying systems, [26][27][28] a variety of gain-scheduled controllers can be synthesized with different degrees of conservativeness. [29][30][31] Efforts to cast the problem of stabilization of nonlinear systems via sampled-data controllers as a set of LMI conditions have been made in the past for Lur'e-type systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Coutinho

Bernal

Palhares

2020

Intl J Robust & Nonlinear

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Robust stabilization of a class of uncertain nonlinear systems through a sampled-data control law is considered in this work. Based on the forward discrete-time Euler approximation, conditions in the form of linear matrix inequalities are provided to synthesize a discrete controller that guarantees the states to be asymptotically driven to the origin, regardless of the presence of bounded parametric uncertainties. In contrast with other approaches, the system is not required to be Lure-type nor the conditions to have predefined gains to be tested. Examples are given to illustrate the effectiveness of the proposal.

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Section: Illustrative Examplesmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Coutinho

Bernal

Palhares

2020

Intl J Robust & Nonlinear

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“…In the case of LPV systems, the non-linearity is embedded in the time-varying parameters that depend on some endogenous signals [14][15][16]. Often, uncertain LTI systems can be seen as a particular case of LPV systems.…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Peixoto

Braga²,

Palhares

2020

IET Control Theory & Appl

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This study addresses the gain-scheduled control problem for discrete-time delayed non-linear parameter-varying (NLPV) and linear parameter-varying (LPV) systems. First, by constructing the parameter-dependent Lyapunov-Krasovskii functional and employing multiple auxiliary functions, delay-dependent reciprocally convex inequality, and selecting a suitable augmented vector, novel delay-dependent linear matrix inequality conditions for the static output-feedback control design and state-feedback control design for delayed NLPV are provided. Second, the results obtained for discrete-time delayed NLPV systems are modified in a simple way to deal with discrete-time delayed LPV systems. Finally, the effectiveness of the proposed methods is illustrated by numerical examples.

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“…Considering time‐varying parameters and system constraints can lead to conservative design results. However, it is possible to reduce the conservativeness by selecting nonquadratic Lyapunov functions, such as parameter‐dependent Lyapunov functions, to perform stability analysis and control synthesis 14‐18 . Alternatively, nonlinear controllers can be used instead of classical linear approaches.…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

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Summary This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ2‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.

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Stability and stabilization for LPV systems based on Lyapunov functions with non-monotonic terms

Cited by 32 publications

References 32 publications

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Robust sampled‐data controller design for uncertain nonlinear systems via Euler discretization

Gain‐scheduled control for discrete‐time non‐linear parameter‐varying systems with time‐varying delays

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

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