5 research outputs found
Affine Parameter-Dependent Lyapunov Functions for LPV Systems with Affine Dependence
This paper deals with the certification problem for robust quadratic
stability, robust state convergence, and robust quadratic performance of linear
systems that exhibit bounded rates of variation in their parameters. We
consider both continuous-time (CT) and discrete-time (DT) parameter-varying
systems. In this paper, we provide a uniform method for this certification
problem in both cases and we show that, contrary to what was claimed
previously, the DT case requires a significantly different treatment compared
to the existing CT results. In the established uniform approach, quadratic
Lyapunov functions, that are affine in the parameter, are used to certify
robust stability, robust convergence rates, and robust performance in terms of
linear matrix inequality feasibility tests. To exemplify the procedure, we
solve the certification problem for -gain performance both in
the CT and the DT cases. A numerical example is given to show that the proposed
approach is less conservative than a method with slack variables.Comment: 8 pages, 3 figure
Affine parameter-dependent Lyapunov functions for LPV systems with affine dependence
This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for L2-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables.</p
Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation
All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version
Model reduction for linear parameter-varying systems through parameter projection
For affine linear parameter-varying (LPV) systems, this paper develops two
parameter reduction methods for reducing the dimension of the parameter space.
The first method achieves the complexity reduction by transforming the affine
LPV system into a parameter-ordered form and establishing an affine upper bound
of the system Gramians, which is extended to time-varying rate-bounded
parameters. The second method is based on considering the sensitivity function
of the transfer function and time evolution equations. Both methods are applied
to an academic example and a thermal model. Simulation results together with
some analysis are given.Comment: This paper has been accepted by 58th IEEE Conference on Decision and
Control (CDC 2019, Nice, France
Affine parameter-dependent Lyapunov functions for LPV systems with affine dependence
\u3cp\u3eThis paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for L2-gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables.\u3c/p\u3