Existence Of Parameter-dependent Lyapunov Function Research Articles

Switching stabilization and $${ H}_{\varvec{\infty }}$$ H ∞ performance of a class of discrete switched LPV system with unstable subsystems

Stability and \(H_\infty \) performance are analyzed in this paper for a class of discrete switched linear parameter-varying (LPV) systems in which all subsystems’ state-space matrices are parametrically affine, and any subsystem is not stable for parameters varying in a convex set. A switching law is designed to stabilize and satisfy the \(H_\infty \) performance of the switched LPV system. By means of the multiple Lyapunov functions method, linear matrix inequality (LMI) conditions for the existence of parameter-dependent Lyapunov functions are proposed. An example shows the effectiveness of the proposed methods.

Parameter-dependent H∞ filter design for LPV systems and an autopilot application

This paper considers the design problem of parameter dependent H ∞ filters for linear parameter varying (LPV) systems whose parameters are measurable. Conditions for existence of parameter-dependent Lyapunov function are proposed via parametrical linear matrix inequality (LMI) constraints. Based on the solutions to the LMIs, an algorithm for the gain matrices of LPV filter is presented. The design method is applied to a missile system to demonstrate the effectiveness.

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties 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.

An improved approach to H-two control with regional stability constraints

This paper presents an improved method for H-two control with regional stability constraints for the closed-loop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.

Robust performance analysis with LMI-based methods for real parametric uncertainty via parameter-dependent Lyapunov functions

Robust performance analysis for linear time-invariant systems with linear fractional transformation real parametric uncertainty is considered. New conditions of robust stability/performance based on parameter-dependent Lyapunov functions are proposed. The robust stability/performance measures are: robust pole location, robust H/sub /spl infin// performance and robust H/sub 2/ performance. Linear matrix inequality (LMI)-based sufficient conditions for the existence of parameter-dependent Lyapunov functions are derived by using the quadratic separation concept. The performances of the proposed conditions are compared with existing tests.

A new robust [formula omitted]-stability condition for real convex polytopic uncertainty

The problem of robust D -stability analysis with respect to real convex polytopic uncertainties is tackled. A new LMI -based sufficient condition for the existence of parameter-dependent Lyapunov functions is proposed. This condition generalises previously published conditions. Numerical comparisons with quadratic stability results as well as previous results based on parameter-dependent Lyapunov functions illustrate the relevance of this new condition. Finally, this result appears to be promising for robust multi-objective performance analysis and control synthesis purposes.

Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions

In this paper, the problem of robust stability of systems subject to parametric uncertainties is considered. Sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion which is reminiscent of, but less conservative than, Popov's stability criterion. An equivalent frequency-domain criterion is demonstrated. The relative sharpness of the proposed test and existing stability criteria is then discussed. The use of parameter-dependent Lyapunov functions for robust controller synthesis is then considered. It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant. A possible synthesis procedure and a numerical example are then discussed.