Izumi Masubuchi

H ∞ control for descriptor systems: a matrix inequalities approach

Abstract This paper considers the H ∞ control problem for descriptor systems that possibly have impulsive modes and/or jω-axis zeros. First, we propose matrix inequalities that give a generalized stability condition and an H ∞ norm condition for descriptor systems. Using these matrix inequalities, we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed H ∞ norm condition as well as stabilizing the closed-loop system and eliminating all impulsive modes. These inequalities are equivalent to certain linear matrix inequalities, to which we can get solutions whenever they exist using efficient polynomial-time algorithms.

LMI‐based controller synthesis: A unified formulation and solution

This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely-known LMIs (for H∞ norm, H2 norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi-objective performance measures, which enable a new formulation of controller design through convex optimization.

Dissipativity inequalities for continuous-time descriptor systems with applications to synthesis of control gains

This paper is concerned with a KYP-type result for descriptor systems. Matrix inequalities are shown that provide necessary and sufficient conditions of dissipativity of descriptor systems, without such restriction on the realization of descriptor systems as in many of previous results. Furthermore, LMI conditions are presented for synthesis of control gains to attain dissipativity of feedback systems represented in the descriptor form.

Gain-scheduled controller design based on descriptor representation of LPV systems: application to flight vehicle control

This paper is concerned with a synthesis method of gain-scheduled controllers based on descriptor representations of LPV systems and its application to design of flight vehicle control. By representing a linear parameter-varying system in the descriptor form, parameter-dependent LMI to seek a gain-scheduled controller are formulated so that they have simple structure with respect to the parameter. A gain-scheduled controller is computed directly via an explicit formula in terms of the variable of LMI for LPV descriptor systems. This synthesis procedure is applied to design of flight vehicle control to satisfy multiple control specifications under large variation of the airspeed. Dynamics of the vehicle is modeled as an LPV descriptor system and a gain-scheduled controller is obtained by solving the proposed LMI. Control performance is improved by employing parameter-dependent Lyapunov matrices.

Synthesis of output feedback gain-scheduling controllers based on descriptor LPV system representation

This paper is concerned with synthesis of gain scheduling control systems based on LPV models in the descriptor form. State-space LPV systems that has coefficient matrices of rational functions of the parameter are equivalent transferred into descriptor LPV systems with coefficient matrices of affine functions. LMI-based controller synthesis approaches for descriptor systems together with computational methods for parameter-dependent LMIs are then applied to design of gain-scheduling controllers with reduced conservatism. Numerical examples are provided to illustrate the proposed approach.

LMI-based output feedback controller design-using a convex parametrization of full-order controllers

This paper proposes a unified output feedback controller synthesis method that employs LMI-represented specifications of H/sub 2/ norm control, H/sub /spl infin// norm control, root clustering and various multiobjective performances. For this purpose, we show a new parametrization of full-order controllers with a convex parameter set, and reduce synthesis problems to solving an LMI on the parameter space.

Spline-type solution to parameter-dependent LMIs

Parameter-dependent quadratic forms (PDQF) play an important role in analysis and synthesis of linear parameter varying (LPV) systems. This paper proposes a method to find a PDQF that meets some criterion written in terms of LMI guaranteeing performances of LPV systems. Through approximation of PDQF with spline functions, we derive finite number of LMI from a given LMI-criterion on a PDQF, which is inherently a condition with infinitely many inequalities. This approximating solution to LMI on a PDQF is proved to have the following properties: (1) any solution to the derived LMI of finite number always produces a PDQF satisfying the original LMI-criterion, and (2) the finite LMI-condition always holds with sufficiently fine division of the parameters region if the original one is solvable. Thus the results of this paper enable to solve parameter-dependent LMI associated with PDQF without conservatism.

Analysis of Positive Invariance and Almost Regional Attraction Via Density Functions With Converse Results

This note is concerned with analysis of positive invariance of nonlinear systems and convergence of trajectories in a region of the state-space via density functions. If there exists a density function that is positive inside a set containing an equilibrium point and tends to zero as approaches to the boundary, the set is positively invariant and almost all of the trajectories starting from there converge to the equilibrium. Converse results are also provided to prove the existence of such density functions.

An LMI condition for stability of implicit systems

This paper considers stability of linear implicit systems. First, we define a stability of implicit systems Ex/spl dot/(t)=Ax(t), where E, A are possibly nonsquare, as with our stability condition the trajectory of the system converges to zero for any initial value admitted by the system. Next, we show an LMI that gives a necessary and sufficient condition for the stability.

PID gain tuning based on falsification using bandpass filters

A data-driven model-free design method of PID gains has been developed based on unfalsified control for a mixed sensitivity control problem. PID gains can be falsified effectively by this method if many sinusoidal responses are used. However, this requires many experiments. In this paper, we propose a method of generating such data that efficiently falsify PID gains by filtering the input output data with many bandpass filters. By this method, PID gains can be falsified effectively from a step response data of a closed-loop system