New Method for SISO Strong Stabilization With Advantages Over Nevanlinna-Pick Interpolation

• 成果类型: Article
• 署名作者: Faruqi, Abdul Hannan; Chatterjee, Anindya
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3538467
• 发表日期: 2025
• 页码: 4774-4779
• 关键词: Poles and zeros; interpolation; SISO; optimization; iterative methods; feedback loop; training; Mechanical engineering; Jacobian matrices; Finite element analysis; Control; linear time-invariant (LTI); single-input-single-output (SISO); strong stabilization

摘要

Linear time-invariant single-input single-output (SISO) systems which satisfy a parity interlacing property (PIP) can be stabilized with a stable controller in a single feedback loop. We consider such stabilization of plants with rational transfer functions of relative degree 0, 1, or 2. Finding such controllers requires an interpolant U(s) with specific properties. Existing methods for finding U(s) use an iterative manual calculation or, when the plant's right half plane zeros are simple, a matrix calculation based on Nevanlinna-Pick interpolation. We present a new interpolant of the form Pi(i)(s+a(i)/s+b(i))(m)(i) , where a(i),b(i)>0 . While our final interpolant has integer m 's, we allow non-integer or real m 's in intermediate calculations. This allows our search to be continuous instead of discrete. Repeated right half plane zeros of the plant are accommodated easily. Real m 's are obtained whenever the plant satisfies the PIP, and integer m 's are obtained for suitably chosen a 's and b 's. With numerical optimization of parameters, the m 's take moderate integer values. We close with some numerical examples.