Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach
From MaRDI portal
Publication:5274015
DOI10.1109/TAC.2005.843848zbMath1365.93365OpenAlexW2161507975MaRDI QIDQ5274015
Andrea Garulli, Graziano Chesi, Antonio Vicino, Alberto Tesi
Publication date: 12 July 2017
Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1109/tac.2005.843848
Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Robust stability (93D09)
Related Items (59)
On homogeneous parameter-dependent quadratic Lyapunov function for robust \(H_\infty\) filtering design in switched linear discrete-time systems with polytopic uncertainties ⋮ A method of estimating the domain of attraction for nonlinear discrete-time systems ⋮ Estimations of the domains of attraction for classes of nonlinear continuous polynomial systems ⋮ On some relaxations commonly used in the study of linear systems ⋮ An alternative Kalman-Yakubovich-Popov lemma and some extensions ⋮ Robust consensus for uncertain multi-agent systems with discrete-time dynamics ⋮ Stability radius of linear parameter-varying systems and applications ⋮ State-feedback disturbance attenuation for polytopic LPV systems with input saturation ⋮ Stability of switched linear systems with possible Zeno behavior: a polytopic approach ⋮ Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions ⋮ Robust stability, ℋ2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix ⋮ Comparisons among robust stability criteria for linear systems with affine parameter uncertainties ⋮ \( H_\infty\) control for continuous-time Takagi-Sugeno fuzzy model by applying generalized Lyapunov function and introducing outer variables ⋮ Stability of uncertain systems using Lyapunov functions with non-monotonic terms ⋮ Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities ⋮ Homogeneous polynomial Lyapunov functions for the analysis of polytopic parameter-dependent descriptor systems ⋮ Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems ⋮ Graph-based conditions for feedback stabilization of switched and LPV systems ⋮ Induced \(\mathcal{L}_2\)-gain computation for rational LPV systems using Finsler's lemma and minimal generators ⋮ On the performance of Kalman filter for Markov jump linear systems with mode mismatch ⋮ On the synthesis of linear \(H_\infty\) filters for polynomial systems ⋮ Fundamental connections among the stability conditions using higher-order time-derivatives of Lyapunov functions for the case of linear time-invariant systems ⋮ Robust control with finite frequency specification for uncertain discrete linear repetitive processes ⋮ Dwell time analysis of deterministic and stochastic switched systems ⋮ On parameter-dependent Lyapunov functions for robust fault detection filter design with application in power systems ⋮ RobustH∞performance using lifted polynomial parameter-dependent Lyapunov functions ⋮ Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions ⋮ Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya's theorem ⋮ Robust performance for uncertain systems via Lyapunov functions with higher order terms ⋮ Parameter-varying state feedback control for discrete-time polytopic systems ⋮ On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems: a counter-example to Barmish's conjecture ⋮ On the stability analysis of nonlinear systems using polynomial Lyapunov functions ⋮ Establishing tightness in robust \(\mathcal H _{\infty}\) analysis via homogeneous parameter-dependent Lyapunov functions ⋮ Parameter-memorized Lyapunov functions for discrete-time systems with time-varying parametric uncertainties ⋮ Fixed-orderH∞controller design for systems with ellipsoidal parametric uncertainty ⋮ Stability analysis and robust performance of periodic discrete-time uncertain systems via structured Lyapunov functions ⋮ Polynomial relaxation-based conditions for global asymptotic stability of equilibrium points of genetic regulatory networks ⋮ Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: asymptotically exact LMI conditions ⋮ A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties ⋮ and filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates ⋮ Matrix sum-of-squares relaxations for robust semi-definite programs ⋮ Robust consensus for linear multi-agent systems with mixed uncertainties ⋮ Time-invariant uncertain systems: a necessary and sufficient condition for stability and instability via homogeneous parameter-dependent quadratic Lyapunov functions ⋮ Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi-Sugeno fuzzy systems ⋮ Performance improvement of robust controllers for polynomially uncertain systems ⋮ LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions ⋮ A new method for robust Schur stability analysis ⋮ Stability analysis of uncertain genetic sum regulatory networks ⋮ Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions ⋮ A generalized parameter-dependent approach to robust \(H _{\infty }\) filtering of stochastic systems ⋮ Algorithm 998 ⋮ On the non-conservatism of a novel LMI relaxation for robust analysis of polytopic systems ⋮ On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach ⋮ Designing parametric linear quadratic regulators for parametric LTI systems via LMIs ⋮ Time-varying discrete-time linear systems with bounded rates of variation: stability analysis and control design ⋮ Robust controllability and observability degrees of polynomially uncertain systems ⋮ Global Stability Analysis of Nonlinear Sampled-Data Systems Using Convex Methods ⋮ and nonquadratic stabilisation of discrete-time Takagi–Sugeno systems based on multi-instant fuzzy Lyapunov functions ⋮ Polynomial optimization with applications to stability analysis and control -- alternatives to sum of squares
This page was built for publication: Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach